This document summarizes research on growing and characterizing thin films of topological insulators. Molecular beam epitaxy was used to deposit films of Bi-Te-Cu(110) and α-Sn-InSb(111)A. Characterization techniques included LEED, AES, STM, and XPS. For Bi-Te-Cu(110), Te did not stick to the substrate and Bi growth was very slow. α-Sn formed islands on InSb(111)A but conditions to form an ordered monolayer were not achieved. Future work involves improving Bi growth conditions and repeating Sn deposition with variations in substrate, temperature, and other materials.