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We present a detailed report of the connection between long-duration gamma-ray bursts (GRBs) and their accompanying supernovae (SNe). The discussion presented here places emphasis on how observations, and the modelling of observations, have constrained what we know about GRB-SNe. We discuss their photometric and spectroscopic properties, their role as cosmological probes, including their measured luminosity–decline relationships, and how they can be used to measure the Hubble constant. We present a statistical summary of their bolometric properties and use this to determine the properties of the “average” GRB-SN. We discuss their geometry and consider the various physical processes that are thought to power the luminosity of GRB-SNe and whether differences exist between GRB-SNe and the SNe associated with ultra-long-duration GRBs. We discuss how observations of their environments further constrain the physical properties of their progenitor stars and give a brief overview of the current theoretical paradigms of their central engines. We then present an overview of the radioactively powered transients that have been photometrically associated with short-duration GRBs, and we conclude by discussing what additional research is needed to further our understanding of GRB-SNe, in particular the role of binary-formation channels and the connection of GRB-SNe with superluminous SNe. [ABSTRACT FROM AUTHOR]