Recent years have seen many examples of how the strong spin-orbit coupling (SOC) present in iridates can stabilize new emergent states that are difficult or impossible to realize in more conventional materials. In this review we outline a representative set of studies detailing how heterostructures based on Ruddlesden-Popper (RP) and perovskite iridates can be used to access yet more novel physics. Beginning with a short synopsis of iridate thin film growth, the effects of the heterostructure morphology on the RP iridates including Sr2IrO4 and SrIrO3 are discussed. Example studies explore the effects of epitaxial strain, laser-excitation to access transient states, topological semimetallicity in SrIrO3, 2D magnetism in artificial RP iridates, and interfacial magnetic coupling between iridate and neighboring layers. Taken together, these works show the fantastic potential for controlled engineering of novel quantum phenomena in iridate heterostructures.