Topology, both in real space and in reciprocal space, has emerged as a new design principle for materials that can host a wealth of novel properties. Examples of topological materials classes discovered over the past few years include three-dimensional topological insulators and three-dimensional Dirac semimetals. Interfaces and heterostructures with three-dimensional topological materials offer opportunities to control and manipulate their electronic states and associated phenomena, for example, via electric field effect, strain, or symmetry breaking. In this presentation, we will discuss recent progress in the growth of thin films of the three-dimensional Dirac semimetal Cd3As2 by molecular beam epitaxy. We show that high-mobility, epitaxial Cd3As2 films can be grown on III-V substrates and discuss some of the phenomena that can be observed, such as an unusually large negative longitudinal magnetoresistance under parallel electric and magnetic fields. These heterostructures allow for experimental tests of theoretically predicted transitions between topological states by manipulating parameters, such as confinement. For example, as the film thickness is reduced, a band gap opens in the bulk Dirac electronic states and we observe the quantum Hall effect that is associated with gapless surface states. If time permits, we will also discuss a completely different type of topological feature, magnetic skyrmions, and their potential realization in oxide thin film heterostructures.