Molecular-beam epitaxy is widely regarded as the gold standard for the synthesisof high-quality complex oxide thin films, yet a broad class of technologically relevant materials has remained out of reach due to fundamental synthesis challenges, chief among them the low vapor pressure of refractory transition metals and the extreme chemical reactivity of alkali elements. This dissertation demonstrates that suboxide MBE, leveraging Ta2O5 and Nb2O5 as volatile molecular beam sources, overcomes these barriers and establishes a general platform for the growth and discovery of complex perovskite oxides with unmatched functional properties. The MBE growth of KTaO3 is first demonstrated using a TaO2 molecular beam generated from a Ta2O5 effusion cell, in conjunction with an airstable In4K intermetallic potassium source. Building on this foundation, compressive biaxial strain imposed by the SrTiO3 (001) substrate is shown to morph the incipient ferroelectric KTaO3 into a ferroelectric with a transition temperature of 475 K. The strain-engineering approach is extended to KNbO3, where compressive biaxial strain suppresses competing polymorphs and stabilizes a single tetragonal phase from 10 K to 975 K, the material’s decomposition temperature in air. This is accompanied by a threefold enhancement in the strain tunability of the Curie temperature relative to all other known perovskite ferroelectrics, a 46% increase in remanent polarization, and a 200% enhancement in optical second-harmonic generation coefficients, establishing strained KNbO3 as a high-performance lead-free ferroelectric. Finally, the suboxide approach is shown to be not merely advantageous but essential for the synthesis of the fractional double perovskite EuTa2O6, a material not achievable from elemental sources. Layered ordering of Eu2+ cations and A-site vacancies along the crystallographic c-axis gives rise to a quasi-two-dimensional electronic structure within a three-dimensional crystal framework, as confirmed by angle-resolved photoemission spectroscopy and density functional theory. Together, these results establish Ta2O5 and Nb2O5 as viable source materials in suboxide MBE.