Abstract:In this article, we will review recent progress in the growth of topological insulator (TI) thin films by molecular beam epitaxy (MBE). The materials we focus on are the V 2 -VI 3 family of TIs. These materials are ideally bulk insulating with surface states housing Dirac excitations which are spin-momentum locked. These surface states are interesting for fundamental physics studies (such as the search for Majorana fermions) as well as applications in spintronics and other fields. However, the majority of TI films and bulk crystals exhibit significant bulk conductivity, which obscures these states. In addition, many TI films have a high defect density. This review will discuss progress in reducing the bulk conductivity while increasing the crystal quality. We will describe in detail how growth parameters, substrate choice, and growth technique influence the resulting TI film properties for binary and ternary TIs. We then give an overview of progress in the growth of TI heterostructures. We close by discussing the bright future for TI film growth by MBE.