The search for a detection of gravitational radiation is now underway. Initial LIGO has already amassed a good amount of data, and its upgraded version. Advanced LIGO, has now been funded and is expected to start operating in 2014. One particularly important class of sources that Advanced LIGO will observe is binary systems made of two black holes. In order to detect these sources, very accurate theoretical models (templates) of the gravitational waveform emitted by these systems are required. In particular, if one or both black holes in the binary are spinning, important dynamical effects due to spins must be taken into account in template waveforms. In this presentation I will focus on the dynamics of the black hole spins themselves. More specifically I will describe the physics behind the main effects which govern the evolution of black hole spins in binaries, and present new developments in analytical understanding of spin dynamics. I will also describe a few more important astrophysical problems for which this recent progress can provide valuable insight.