  Recent developments in multi-dimensional simulations of core-collapse
supernovae have considerably improved our understanding of this complex
phenomenon. In addition to that, one-dimensional (1D) studies have been
employed to study the explosion mechanism and its causal connection to the
pre-collapse structure of the star, as well as to explore the vast parameter
space of supernovae. Nonetheless, many uncertainties still affect the late
stages of the evolution of massive stars, their collapse, and the subsequent
shock propagation. In this review, we will briefly summarize the
state-of-the-art of both 1D and 3D simulations and how they can be employed to
study the evolution of massive stars, supernova explosions, and shock
propagation, focusing on the uncertainties that affect each of these phases.
Finally, we will illustrate the typical nucleosynthesis products that emerge
from the explosion.
