At low enough temperatures and at microscopic length scales the laws of quantum mechanics become apparent. The underlying superposition principle leads to interference phenomena for one degree of freedom and to the concept of entanglement for two and more. Entangled degrees of freedom are often correlated beyond their classically allowed correlation. These quantum correlations also appear in very large systems and are caused by strong interactions between the constituents. Strongly correlated forms of quantum matter became ubiquitous in condensed matter physics, with the discovery of heavy fermion materials, cuprates and other unconventional superconductors. Here the main players are electrons embedded in solid matter. But they also can be found in interacting quantum gases, where the main players are atoms. In the latter case the required temperatures for quantum correlations to appear are much lower. But in turn the length scales are larger and they can be embedded in well controlled potentials. A fascinating possibility offered by present day technologies is to tailor matter in order to induce the emergence of new phenomena by controlling quantum correlations. One of the routes leading to spectacular advances is the configuration of nanomaterials like quantum dots or quantum wires on the basis of semiconducting substrates that allow, e.g., to manipulate the Kondo effect or Luttinger liquids affecting transport properties through such nanostructures. Another quite different route with at the moment unlimited potential is offered by quantum optics and atomic physics, when implemented to bring quantum gases into the strongly interacting regime. This can be achieved by optical lattices leading to Mott-insulators, or to two dimensional systems displaying Kosterlitz–Thouless behavior in bosonic gases, or by Feshbach resonances, leading to fermionic systems with unconventional superfluid states like the Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) one. In spite of the very different experimental realizations leading to the two routes mentioned above, they share a common goal, namely achieving a deep understanding of quantum correlations that will ultimately allow to control them and possibly realize new forms of matter. They also share the flexibility that allows to increase the complexity in quantum correlations by joining in a controlled manner well understood building units and/or by regulating their coupling to the environment. It is under the common goal of understanding and controlling quantum correlations that we see the topics presented in this focus issue of New Journal of Physics, where both lines of development, that is on solid-state substrates or with quantum gases, give a timely view of the advances towards the above mentioned common goal. Focus on Quantum Correlations in Tailored Matter Contents Temperature changes when adiabatically ramping up an optical lattice Lode Pollet, Corinna Kollath, Kris Van Houcke and Matthias Troyer Numerical study of two-body correlation in a 1D lattice with perfect blockade B Sun and F Robicheaux Kinetic Monte Carlo modeling of dipole blockade in Rydberg excitation experiment Amodsen Chotia, Matthieu Viteau, Thibault Vogt, Daniel Comparat and Pierre Pillet Motion of Rydberg atoms induced by resonant dipole–dipole interactions C Ates, A Eisfeld and J M Rost Quantum coherence due to Bose–Einstein condensation of parametrically driven magnons S O Demokritov, V E Demidov, O Dzyapko, G A Melkov and A N Slavin Chaotic dynamics in spinor Bose–Einstein condensates J Kronjager, K Sengstock and K Bongs Damped Bloch oscillations of Bose–Einstein condensates in disordered potential gradients S Drenkelforth, G Kleine Buning, J Will, T Schulte, N Murray, W Ertmer, L Santos and J J Arlt Rabi oscillations between ground and Rydberg states and van der Waals blockade in a mesoscopic frozen Rydberg gas M Reetz-Lamour, J Deiglmayr, T Amthor and M Weidemuller Excitations in two-component Bose gases A Kleine, C Kollath, I P McCulloch, T Giamarchi and U Schollwock Exploring the growth of correlations in a quasi one-dimensional trapped Bose gas M Eckart, R Walser and W P Schleich How to fix a broken symmetry: quantum dynamics of symmetry restoration in a ferromagnetic Bose–Einstein condensate Bogdan Damski and Wojciech H Zurek Landau levels of cold atoms in non-Abelian gauge fields A Jacob, P Ohberg, G Juzeliunas and L Santos Atomic four-wave mixing via condensate collisions A Perrin, C M Savage, D Boiron, V Krachmalnicoff, C I Westbrook and K V Kheruntsyan Semifluxons in superconductivity and cold atomic gases R Walser, E Goldobin, O Crasser, D Koelle, R Kleiner and W P Schleich Disorder-induced trapping versus Anderson localization in Bose–Einstein condensates expanding in disordered potentials L Sanchez-Palencia, D Clement, P Lugan, P Bouyer and A Aspect Critical tunneling currents in the regime of bilayer excitons L Tiemann, W Dietsche, M Hauser and K von Klitzing Quantum phases of trapped ions in an optical lattice R Schmied, T Roscilde, V Murg, D Porras and J I Cirac Generation and detection of a spin entanglement in nonequilibrium quantum dots Stefan Legel, Jurgen Konig and Gerd Schon Slow light in inhomogeneous and transverse fields Leon Karpa and Martin Weitz FFLO state in 1-, 2- and 3-dimensional optical lattices combined with a non-uniform background potential T K Koponen, T Paananen, J-P Martikainen, M R Bakhtiari and P Torma Geometry-dependent interplay of long- and short-range interactions in ultracold fermionic gases: models for condensed matter and astrophysics B Deb, G Kurizki and I E Mazets Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids V Meden, S Andergassen, T Enss, H Schoeller and K Schonhammer Luttinger hydrodynamics of confined one-dimensional Bose gases with dipolar interactions R Citro, S De Palo, E Orignac, P Pedri and M-L Chiofalo Towards deterministically controlled InGaAs/GaAs lateral quantum dot molecules L Wang, A Rastelli, S Kiravittaya, P Atkinson, F Ding, C C Bof Bufon, C Hermannstadter, M Witzany, G J Beirne, P Michler and O G Schmidt Effective parameters for weakly coupled Bose–Einstein condensates S Giovanazzi, J Esteve and M K Oberthaler Current statistics of correlated charge tunnelling through an impurity in a 1D wire Alexander Herzog and Ulrich Weiss Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap Stephan A Schulz, Ulrich Poschinger, Frank Ziesel and Ferdinand Schmidt-Kaler The trapped two-dimensional Bose gas: from Bose–Einstein condensation to Berezinskii–Kosterlitz–Thouless physics Z Hadzibabic, P Kruger, M Cheneau, S P Rath and J Dalibard Dynamical protection of quantum computation from decoherence in laser-driven cold-ion and cold-atom systems Goren Gordon and Gershon Kurizki Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond Ph Tamarat, N B Manson, J P Harrison, R L McMurtrie, A Nizovtsev, C Santori, R G Beausoleil, P Neumann, T Gaebel, F Jelezko, P Hemmer and J Wrachtrup Superconductivity in the attractive Hubbard model: functional renormalization group analysis R Gersch, C Honerkamp and W Metzner Quantum stability of Mott-insulator states of ultracold atoms in optical resonators Jonas Larson, Sonia Fernandez-Vidal, Giovanna Morigi and Maciej Lewenstein