Molecular beam epitaxy technique has enabled synthesis of atomically smooth thin films, multilayers, and superlattices of cuprates and other complex oxides. Such heterostructures show high temperature superconductivity and enable novel experiments that probe the basic physics of this phenomenon. For example, it was established that high temperature superconductivity and anti-ferromagnetic phases separate on Ångström scale, while the pseudo-gap state apparently mixes with high temperature superconductivity over an anomalously large length scale (the “Giant Proximity Effect”). We review some recent experiments on such films and superlattices, including X-ray diffraction, atomic force microscopy, angle-resolved time of flight ion scattering and recoil spectroscopy, transport measurements, high- resolution transmission electron microscopy, resonant X-ray scattering, low-energy muon spin resonance, and ultrafast photo-induced reflection high energy electron diffraction. The results include an unambiguous demonstration of strong coupling of in-plane charge excitations to out-of-plane lattice vibrations, a discovery of interface high temperature superconductivity that occurs in a single CuO2 plane, evidence for local pairs, and establishing tight limits on the temperature range of superconducting fluctuations.