Gravitational-wave observations have revealed the population of stellar remnants from a new angle. Yet their stellar progenitors remain uncertain, in particular in the case of black holes. At least a fraction of these progenitors is believed to form in isolated binary systems. In this talk, I will discuss how binary mass transfer affects the late evolution and final fate of massive stars. The focus will be on stars that transfer their outer layers to a companion star and become binary-stripped. Binary-stripped stars develop systematically different core structures compared to single stars. I will discuss consequences for supernova progenitors, black hole formation, supernova nucleosynthesis, and gravitational-wave observations.