Incorporating our best understanding of binary evolution is critical for interpreting the growing sample of gravitational-wave sources. Although rapid binary population synthesis codes have been used for decades to investigate the complex evolution of binary black holes, they typically rely on analytical fits of single-star evolutionary tracks and parameterized models for interactive phases of evolution. In this talk I will show how using detailed simulations with MESA, compared to using rapid binary population synthesis codes, changes the predicted formation paths and the orbital periods of merging binary black holes, and consequently their merger rates. I will also discuss the formation paths leading to non-spinning LIGO sources and high-spinning BHs in high-mass X-ray binaries.