Core-collapse supernovae (CCSNe) are the explosions that attend the deaths of massive stars. Despite decades of research, several aspects of the mechanism that drives these explosions remain uncertain and the subjects of continued investigation. In this short review, I will give an overview of the CCSN mechanism and current research in the field. In particular, I will focus on recent results from three-dimensional simulations and the impact of turbulence and detailed non-spherical progenitor structure on CCSNe. This contribution is based on a talk given at the ‘Bridging the Gap’ workshop at Chicheley Hall on 2 June 2016.This article is part of the themed issue ‘Bridging the gap: from massive stars to supernovae’.