When a core-collapse supernova explodes, it ejects elements synthesized during the post-main-sequence evolution of the star, and it produces new elements during the explosion (the so-called explosion nucleosynthesis). In the aftermath of the explosion, a neutron star is left behind. How massive the leftover neutron star is, and how much mass of each element is ejected during the explosion are two of the questions I will address during this talk. The neutron star mass distribution impacts the remnant population of the galaxy, and therefore is a key input for population synthesis studies (for example, it makes up the seeds for neutron star merger events). The ejected elements contribute to enriching the interstellar medium, which is used to form the next generation of stars, and can therefore be observed in their photosphere. One of the biggest uncertainties in predicting both remnant masses and nucleosynthetic yields is the explodability, i.e., which stars explode? Which ones do not and, instead, end up as failed supernovae, forming a black hole? Only state-ofthe-art models of the explosion can answer this question. In this talk, I will present recent results using 1D simulations that include sophisticated neutrino transport, general relativistic effects, and a mixing-length theory model for neutrino-driven convection, which, as I will show, is a key aspect in the explosion.