From 1D to 3D simulations: the pursuit to model the spins and tilts of stellar-mass black holes*

Understanding the spin magnitudes and tilts of stellar-mass black holes is crucial for unraveling their evolutionary histories. As the sensitivity of electromagnetic telescopes and gravitational wave detectors increases, we will gain precise measurements of these properties for both Galactic and high-redshift populations. To make sense of this data, we must accurately model the physical processes that are responsible for shaping the spins and tilts of these stellar-mass black holes. This pursuit demands a multitude of methodologies and theoretical perspectives. In this talk, I will review the existing models for both spin magnitudes and tilts, exploring insights gained from theoretical studies on stellar and binary evolution, as well as accretion disk simulations. I will highlight what these studies have revealed about the spins and tilts of stellar-mass black holes and outline the questions we need to address in our pursuit of a comprehensive understanding of the formation and lives of stellar-mass black holes.