Galaxies live in a range of environments, characterized by their volume density. For example, the densest regions of the Universe are in galaxy clusters, which contain hundreds to thousands of galaxies all in pseudo-gravitational virial equilibrium. These dense environments can in turn alter the properties of the galaxies themselves in striking ways via a variety of gravitational and hydrodynamic processes. The result of these processes alter galaxy shapes, their internal dynamics, and shuts off the formation of new stars. I will present work I have been doing to characterize the evolution of galaxies in clusters over the past 10 billion years as a way of understanding how the environment can affect galaxies. I will describe how we have used extensive multi-wavelength data sets on distant clusters to form a picture in which infalling cluster galaxies likely have their gas supplies cut off, their morphologies transformed, and may even experience epochs of very frequent mergers. I will also discuss new results on molecular gas observations of distant cluster and proto-cluster galaxies that I am using to understand how the quenching of star formation in massive cluster galaxies proceeds at the epoch when they began their final cessation of star formation.