Using the redMaPPer catalog of 21709 galaxy clusters and photometric information for 455946 galaxies from SDSS DR8, we study the effects of local and global environment on galaxy evolution within clusters in the redshift range 0.2 ≤ z ≤ 0.5 and the richness range 20 ≤ λ ≤ 236. We use cluster richness λ as a proxy for global environment and cluster-centric radius dBCG to represent the local environ- ment within clusters. We measure giant-to-dwarf ratio (GDR) which gives insight regarding the composition of the red sequence, and we measure red fraction which holds information about the rate at which galaxies falling into clusters cease to form new stars and build up the red sequence in a phenomenon called quenching. We ob- serve that red fraction decreases with redshift, increases with λ, and decreases with dBCG. GDR, meanwhile, decreases with redshift, does not vary significantly with λ, and decreases with dBCG. All together, our results tell the story of clusters starting with bright, massive galaxies which accrete smaller and smaller galaxies over time. The galaxies are quickly quenched upon entering clusters environment. We observe that most quenching occurs on smaller richness scales than our data covers, and that by the time clusters have grown to the richnesses redMaPPer is sensitive to, ram pressure stripping is likely to be the dominant quenching mechanism. / Graduate