Ozone-assisted molecular beam epitaxy (MBE) has been developed for growing high-Tc superconducting films. It involves the co-evaporation of their elemental constituents together with the use of ozone as a source of reactive oxygen. The advantage of using ozone over other forms of reactive oxygen is that it is stable enough to be prepared and delivered to the substrate in a very pure form using very simple apparatus, providing a well-characterized flow of oxidizing gas. Using ozone, a post-deposition anneal is not needed to produce films with high transition temperatures, and growth can be carried out at relatively low system pressures. As a consequence, the surface analysis using reflection high energy electron diffraction is possible during film growth. Recent refinements of ozone-assisted MBE directed at the YBa2Cu3O7-σ family of films are described here. The results indicate that this technique is very competitive for growing the highest quality superconducting films and should be ideal for fabricating structures.