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Full list of authors: Acciari, V. A.; Ansoldi, S.; Antonelli, L. A.; Arbet Engels, A.; Artero, M.; Asano, K.; Babić, A.; Baquero, A.; Barres de Almeida, U.; Barrio, J. A.; Batković, I.; Becerra González, J.; Bednarek, W.; Bellizzi, L.; Bernardini, E.; Bernardos, M.; Berti, A.; Besenrieder, J.; Bhattacharyya, W.; Bigongiari, C.; Blanch, O.; Bošnjak, Ž.; Busetto, G.; Carosi, R.; Ceribella, G.; Cerruti, M.; Chai, Y.; Chilingarian, A.; Cikota, S.; Colak, S. M.; Colombo, E.; Contreras, J. L.; Cortina, J.; Covino, S.; D'Amico, G.; D'Elia, V.; da Vela, P.; Dazzi, F.; de Angelis, A.; de Lotto, B.; Delfino, M.; Delgado, J.; Delgado Mendez, C.; Depaoli, D.; di Pierro, F.; di Venere, L.; Do Souto Espiñeira, E.; Dominis Prester, D.; Donini, A.; Doro, M.; Fallah Ramazani, V.; Fattorini, A.; Ferrara, G.; Fonseca, M. V.; Font, L.; Fruck, C.; Fukami, S.; García López, R. J.; Garczarczyk, M.; Gasparyan, S.; Gaug, M.; Giglietto, N.; Giordano, F.; Gliwny, P.; Godinović, N.; Green, J. G.; Green, D.; Hadasch, D.; Hahn, A.; Heckmann, L.; Herrera, J.; Hoang, J.; Hrupec, D.; Hütten, M.; Inada, T.; Inoue, S.; Ishio, K.; Iwamura, Y.; Jiménez, I.; Jormanainen, J.; Jouvin, L.; Kajiwara, Y.; Karjalainen, M.; Kerszberg, D.; Kobayashi, Y.; Kubo, H.; Kushida, J.; Lamastra, A.; Lelas, D.; Leone, F.; Lindfors, E.; Lombardi, S.; Longo, F.; López-Coto, R.; López-Moya, M.; López-Oramas, A.; Loporchio, S.; Machado de Oliveira Fraga, B.; Maggio, C.; Majumdar, P.; Makariev, M.; Mallamaci, M.; Maneva, G.; Manganaro, M.; Maraschi, L.; Mariotti, M.; Martínez, M.; Mazin, D.; Menchiari, S.; Mender, S.; Mićanović, S.; Miceli, D.; Miener, T.; Minev, M.; Miranda, J. M.; Mirzoyan, R.; Molina, E.; Moralejo, A.; Morcuende, D.; Moreno, V.; Moretti, E.; Neustroev, V.; Nigro, C.; Nilsson, K.; Nishijima, K.; Noda, K.; Nozaki, S.; Ohtani, Y.; Oka, T.; Otero-Santos, J.; Paiano, S.; Palatiello, M.; Paneque, D.; Paoletti, R.; Paredes, J. M.; Pavletić, L.; Peñil, P.; Perennes, C.; Persic, M.; Prada Moroni, P. G.; Prandini, E.; Priyadarshi, C.; Puljak, I.; Ribó, M.; Rico, J.; Righi, C.; Rugliancich, A.; Saha, L.; Sahakyan, N.; Saito, T.; Sakurai, S.; Satalecka, K.; Saturni, F. G.; Schmidt, K.; Schweizer, T.; Sitarek, J.; Šnidarić, I.; Sobczynska, D.; Spolon, A.; Stamerra, A.; Strom, D.; Strzys, M.; Suda, Y.; Surić, T.; Takahashi, M.; Tavecchio, F.; Temnikov, P.; Terzić, T.; Teshima, M.; Tosti, L.; Truzzi, S.; Tutone, A.; Ubach, S.; van Scherpenberg, J.; Vanzo, G.; Vazquez Acosta, M.; Ventura, S.; Verguilov, V.; Vigorito, C. F.; Vitale, V.; Vovk, I.; Will, M.; Wunderlich, C.; Zarić, D.; Baack, D.; Balbo, M.; Biederbeck, N.; Biland, A.; Bretz, T.; Buss, J.; Dorner, D.; Eisenberger, L.; Elsaesser, D.; Hildebrand, D.; Iotov, R.; Mannheim, K.; Neise, D.; Noethe, M.; Paravac, A.; Rhode, W.; Schleicher, B.; Sliusar, V.; Walter, R.; D'Ammando, F.; Horan, D.; Lien, A. Y.; Baloković, M.; Madejski, G. M.; Perri, M.; Verrecchia, F.; Leto, C.; Lähteenmäki, A.; Tornikoski, M.; Ramakrishnan, V.; Järvelä, E.; Vera, R. J. C.; Chamani, W.; Villata, M.; Raiteri, C. M.; Gupta, A. C.; Pandey, A.; Fuentes, A.; Agudo, I.; Casadio, C.; Semkov, E.; Ibryamov, S.; Marchini, A.; Bachev, R.; Strigachev, A.; Ovcharov, E.; Bozhilov, V.; Valcheva, A.; Zaharieva, E.; Damljanovic, G.; Vince, O.; Larionov, V. M.; Borman, G. A.; Grishina, T. S.; Hagen-Thorn, V. A.; Kopatskaya, E. N.; Larionova, E. G.; Larionova, L. V.; Morozova, D. A.; Nikiforova, A. A.; Savchenko, S. S.; Troitskiy, I. S.; Troitskaya, Y. V.; Vasilyev, A. A.; Merkulova, O. A.; Chen, W. P; Samal, M.; Lin, H. C.; Moody, J. W.; Sadun, A. C.; Jorstad, S. G.; Marscher, A. P.; Weaver, Z. R.; Feige, M.; Kania, J.; Kopp, M.; Kunkel, L.; Reinhart, D.; Scherbantin, A.; Schneider, L.; Lorey, C.; Acosta-Pulido, J. A.; Carnerero, M. I.; Carosati, D.; Kurtanidze, S. O.; Kurtanidze, O. M.; Nikolashvili, M. G.; Chigladze, R. A.; Ivanidze, R. Z.; Kimeridze, G. N.; Sigua, L. A.; Joner, M. D.; Spencer, M.; Giroletti, M.; Marchili, N.; Righini, S.; Rizzi, N.; Bonnoli, G.; MAGIC Collaboration; Fact Collaboration.-- This is an Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited., Aims. We present a detailed characterisation and theoretical interpretation of the broadband emission of the paradigmatic TeV blazar Mrk 421, with a special focus on the multi-band flux correlations. Methods. The dataset has been collected through an extensive multi-wavelength campaign organised between 2016 December and 2017 June. The instruments involved are MAGIC, FACT, Fermi-LAT, Swift, GASP-WEBT, OVRO, Medicina, and Metsahovi. Additionally, four deep exposures (several hours long) with simultaneous MAGIC and NuSTAR observations allowed a precise measurement of the falling segments of the two spectral components. Results. The very-high-energy (VHE; E 100 GeV) gamma rays and X-rays are positively correlated at zero time lag, but the strength and characteristics of the correlation change substantially across the various energy bands probed. The VHE versus X-ray fluxes follow dierent patterns, partly due to substantial changes in the Compton dominance for a few days without a simultaneous increase in the X-ray flux (i.e., orphan gamma-ray activity). Studying the broadband spectral energy distribution (SED) during the days including NuSTAR observations, we show that these changes can be explained within a one-zone leptonic model with a blob that increases its size over time. The peak frequency of the synchrotron bump varies by two orders of magnitude throughout the campaign. Our multi-band correlation study also hints at an anti-correlation between UV-optical and X-ray at a significance higher than 3. A VHE flare observed on MJD 57788 (2017 February 4) shows gamma-ray variability on multi-hour timescales, with a factor ten increase in the TeV flux but only a moderate increase in the keV flux. The related broadband SED is better described by a two-zone leptonic scenario rather than by a one-zone scenario.We find that the flare can be produced by the appearance of a compact second blob populated by high energetic electrons spanning a narrow range of Lorentz factors, from 0 min = 2104 to 0 max = 6105. © 2021 Georg Thieme Verlag. All rights reserved., The MAGIC Collaboration would like to thank the Instituto de Astrofísica de Canarias for the excellent working conditions at the Observatorio del Roque de los Muchachos in La Palma. The financial support of the German BMBF, MPG and HGF; the Italian INFN and INAF; the Swiss National Fund SNF; the ERDF under the Spanish Ministerio de Ciencia e Innovación (MICINN) (FPA2017-87859-P, FPA2017-85668-P, FPA2017-82729-C6-5-R, FPA2017-90566-REDC, PID2019-104114RB-C31, PID2019-104114RB-C32, PID2019-105510GB-C31,PID2019-107847RB-C41, PID2019-107847RB-C42, PID2019-107847RB-C44, PID2019-107988GB-C22); the Indian Department of Atomic Energy; the Japanese ICRR, the University of Tokyo, JSPS, and MEXT; the Bulgarian Ministry of Education and Science, National RI Roadmap Project DO1-268/16.12.2019 and the Academy of Finland grant nr. 320045 is gratefully acknowledged. This work was also supported by the Spanish Centro de Excelencia “Severo Ochoa” SEV-2016-0588, SEV-2017-0709 and CEX2019-000920-S, and “María de Maeztu” CEX2019-000918-M, the Unidad de Excelencia “María de Maeztu” MDM-2015-0509-18-2 and the “la Caixa” Foundation (fellowship LCF/BQ/PI18/11630012) and by the CERCA program of the Generalitat de Catalunya; by the Croatian Science Foundation (HrZZ) Project IP-2016-06-9782 and the University of Rijeka Project 13.12.1.3.02; by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3; the Polish National Research Centre grant UMO-2016/22/M/ST9/00382; and by the Brazilian MCTIC, CNPq and FAPERJ. The important contributions from ETH Zurich grants ETH-10.08-2 and ETH-27.12-1 as well as the funding by the Swiss SNF and the German BMBF (Verbundforschung Astro- und Astroteilchenphysik) and HAP (Helmoltz Alliance for Astroparticle Physics) are gratefully acknowledged. Part of this work is supported by Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center SFB 876 “Providing Information by Resource-Constrained Analysis”, project C3. We are thankful for the very valuable contributions from E. Lorenz, D. Renker and G. Viertel during the early phase of the project. We thank the Instituto de Astrofísica de Canarias for allowing us to operate the telescope at the Observatorio del Roque de los Muchachos in La Palma, the Max-Planck-Institut für Physik for providing us with the mount of the former HEGRA CT3 telescope, and the MAGIC collaboration for their support. The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. This work performed in part under DOE Contract DE-AC02-76SF00515. This work made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software, and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC; Italy) and the California Institute of Technology (USA). This research has also made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASI Science Data Center (ASDC), Italy. A.A.E and D.P acknowledge support from the Deutsche Forschungs gemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2094 – 390783311. M. B. acknowledges support from the YCAA Prize Postdoctoral Fellowship and from the Black Hole Initiative at Harvard University, which is funded in part by the Gordon and Betty Moore Foundation (grant GBMF8273) and in part by the John Templeton Foundation. This publication makes use of data obtained at the Metsähovi Radio Observatory, operated by Aalto University in Finland. This research has made use of data from the OVRO 40-m monitoring program (Richards et al. 2011) which is supported in part by NASA grants NNX08AW31G, NNX11A043G, and NNX14AQ89G and NSF grants AST-0808050 and AST-1109911. I.A. acknowledges financial support from the Spanish “Ministerio de Ciencia e Innovación” (MCINN) through the “Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de Andalucía-CSIC (SEV-2017-0709). Acquisition and reduction of the MAPCAT data was supported in part by MICINN through grants AYA2016-80889-P and PID2019-107847RB-C44. The MAPCAT observations were carried out at the German-Spanish Calar Alto Observatory, which is jointly operated by Junta de Andalucía and Consejo Superior de Investigaciones Científicas. C.C. acknowledges support from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program under the grant agreement No 771282. This research was partially supported by the Bulgarian National Science Fund of the Ministry of Education and Science under grants KP-06-H28/3 (2018), KP-06-H38/4 (2019) and KP-06-KITAJ/2 (2020). We acknowledge support by Bulgarian National Science Fund under grant DN18-10/2017 and National RI Roadmap Projects DO1-277/16.12.2019 and DO1-268/16.12.2019 of the Ministry of Education and Science of the Republic of Bulgaria. This research was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (contract No 451-03-68/2020-14/200002). G.D. acknowledges observing grant support from the Institute of Astronomy and Rozhen NAO BAS through the bilateral joint research project “Gaia Celestial Reference Frame (CRF) and fast variable astronomical objects” (2020–2022, head – G. Damljanovic). The BU group was supported in part by NASA Fermi guest investigator program grants 80NSSC19K1505 and 80NSSC20K1566. This study was based in part on observations conducted using the 1.8 m Perkins Telescope Observatory (PTO) in Arizona, which is owned and operated by Boston University. This article is partly based on observations made with the LCOGT Telescopes, one of whose nodes is located at the Observatorios de Canarias del IAC on the island of Tenerife in the Observatorio del Teide. This article is also based partly on data obtained with the STELLA robotic telescopes in Tenerife, an AIP facility jointly operated by AIP and IAC. The Abastumani team acknowledges financial support by the Shota Rustaveli National Science Foundation under contract FR-19-6174. Based on observations with the Medicina telescope operated by INAF – Istituto di Radioastronomia.