In this thesis we present two projects investigating the evolution and quenching of cluster galaxy star formation (SF) activity. Leveraging a sample of 36 galaxy clusters, we measure the level of member SF activity. Over the 7.5 billion years spanned by our clusters, from z=1.5 to z=0.15, the SF activity of cluster galaxies decreases by a factor of 11. This is much larger than the three-fold decline experienced by star-forming galaxies (SFGs), or the factor of four drop for quiescent galaxies, which have SF activity more than an order of magnitude lower than SFGs. The overall evolution of cluster member SF activity is driven not by the decline of either subset, but instead by the transitioning of galaxies from star-forming to quiescence. Indeed, from z=1.5 to z=0.15, the fraction of quiescent galaxies rises from 28% to 88%. To investigate the impact of strangulation, a long timescale quenching mechanism, we determine whether 58 members of the nearby galaxy cluster Abell 1795 possess hot halos. Markov chain Monte Carlo sampling is used to fit surface brightness profiles (SBPs) of stacked X-ray images with models that account for the dominant X-ray emission in and around cluster members. Hot gas halos around outer Abell 1795 members are detected, in a statistical sense. Inner cluster hot halos, however, remain undetected, with a luminosity upper limit six times lower than the hot halo luminosity in the outer cluster. This suggests that Abell 1795's intracluster medium is likely stripping the hot gas halos of infalling members. To further test our modeling technique we apply it to five additional clusters. Combining their data, we generate profiles and retrieve a good fit to the inner cluster SBP. Due to a relative lack of data in the clusters' outskirts, we are unable to provide much constraint on hot halo presence. We propose stacking a greater number of outer cluster members, which would necessitate acquiring additional X-ray data, likely through a more targeted search of the Chandra Data Archive.