One of the defining features of the last 8-10 billion years of cosmic history is the emergence of a red sequence of non-star-forming galaxies. In spite of considerable theoretical and observational work, there is still no consensus on what causes blue galaxies to stop forming stars and transition onto the red sequence. To gain insight into the processes at work, we have been studying samples of galaxies in the midst of star formation quenching. We have identified post-starburst galaxies spectroscopically at z~0.1, 0.4, and 0.6 from SDSS-I and SDSS-III/BOSS. I will discuss the relationship between post-starbursts and galaxy mergers, and the role of AGN and star-formation driven galactic winds in truncating star formation.