In order for black-hole binaries, neutron-star binaries, and black-hole-neutron-star binaries to merge within a Hubble time, they need to be brought to a close-enough separation that gravitational radiation is strong enough to drive inspiral. For compact binaries that form in isolation, the progenitors need to survive two supernova explosions and one or more common-envelope phases. I will describe our current efforts on simulating common-envelope evolution of massive-star binaries with global 3D radiation-hydrodynamical simulations. For the proposed massive-star progenitors of heavy stellar-mass black-hole binaries, we find that the common-envelope phase does not exhibit a rapid plunge as often seen in low-mass cases. I will then discuss our recent results on supernova natal kicks in close binaries, where gravitational radiation from such kicks may radiate away a significant fraction of binary's orbital energy away in gravitational waves.