The broad emission lines in the spectra of active galactic nuclei respond to variations in the luminosity of the central continuum source with a delay due to light-travel time effects within the emission-line region. It is therefore possible through the process of 'reverberation mapping' to determine the geometry and kinematics of the emission-line region by careful monitoring of the continuum variations and the resulting emission-line response. In this review, I will discuss progress in application of the reverberation mapping technique. I will describe the underlying assumptions and limitations of the method, discuss how the results obtained to date are changing our understanding of active nuclei, and outline several new questions that might be addressed through further reverberation mapping programs.