  In this review we present a progress report of the connection between
long-duration gamma-ray bursts (GRBs) and their accompanying supernovae (SNe).
The analysis 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-SNe: which has a kinetic energy of $E_{\rm K} \approx
2.5\times10^{52}$ erg, an ejecta mass of $M_{\rm ej} \approx 6$ M$_{\odot}$, a
nickel mass of $M_{\rm Ni} \approx 0.4$ M$_{\odot}$, a peak photospheric
velocity of $v_{\rm ph} \approx 21,000$ km s$^{-1}$, a peak bolometric
luminosity of $L_{\rm p} \approx 1\times10^{43}$ erg s$^{-1}$, and it reaches
peak bolometric light in $t_{\rm p} \approx 13$ days. We discuss their
geometry, 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
the environments of GRB-SNe further constrain the physical properties of their
progenitor stars, and give an overview of the current theoretical paradigms of
their suspected central engines. We also present an overview of the
radioactively powered transients that have been photometrically associated with
short-duration GRBs. 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 (abridged).
