In this review article we present an up-to-date progress report of the connection between long-duration (and their various sub-classes) gamma-ray bursts (GRBs) and their accompanying supernovae (SNe). The analysis presented here is from the point of view of an observer, with much of the emphasis placed on how observations, and the modelling of observations, have constrained what we known 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 analysis of their bolometric properties, and use this to determine the properties of the "average" GRB-SN: which has a kinetic energy of E K ≈ 2.5 × 10 52 erg (σ E K = 1.8 × 10 52 erg), an ejecta mass of M ej ≈ 6 M (σ M ej = 4 M ), a nickel mass of M Ni ≈ 0.4 M (σ M Ni = 0.2 M ), an ejecta velocity at peak light of v ≈ 20, 000 km s −1 (σ v ph = 8, 000 km s −1 ), a peak bolometric luminosity of L p ≈ 1×10 43 erg s −1 (σ Lp = 0.4×10 43 erg s −1 ), and it reaches peak bolometric light in t p ≈ 13 days (σ tp = 2.7 days). We discuss their geometry, as constrained from observations, 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 such as GRB 111209A/SN 2011kl. We discuss how observations of the environments of GRB-SNe further constrain the physical properties of their pre-explosion progenitor stars, and give a brief overview of the current theoretical paradigms of the central engines that produce the various types of GRB-SNe. Furthermore, we present an overview of the r-process, radioactively powered transients that have been photometrically associated with short-duration GRBs, and we conclude the review 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. arXiv:1604.03549v2 [astro-ph.HE] 18 Jul 2016 1 A: Strong spectroscopic evidence. B: A clear light curve bump as well as some spectroscopic evidence resembling a GRB-SN. C: A clear bump consistent with other GRB-SNe at the spectroscopic redshift of the GRB. D: A bump, but the inferred SN properties are not fully consistent with other GRB-SNe or the bump was not well sampled or there is no spectroscopic redshift of the GRB. E: A bump, either of low significance or inconsistent with other GRB-SNe. * Denotes exact, K-corrected rest-frame filter observable. ‡ Values fixed during fit.k ands denote the filter-averaged luminosity (k) and stretch (s) factors relative to SN 1998bw.