Perovskite oxide (ABO3 type compounds) is an important class of materials exhibiting a wide range of functionalities. However, in comparison to conventional semiconductors such as silicon, they possess orders of magnitude lower room-temperature electron mobilities. For example, in doped SrTiO3, the best reported room-temperature value of electron mobility has remained below 10 cm2 V−1 s−1 for over five decades. The realization of a perovskite oxide semiconductor with high room-temperature mobility would constitute a significant advancement, enabling novel physical and perhaps even a plethora of new and more realistic device concepts. Very recently a key step in this direction was taken via the growth of bulk doped BaSnO3, where room-temperature mobilities as high as 320 cm2 V−1 s−1 was reported. Thin films of BaSnO3 show much lower room-temperature mobility values ranging between 1-180 cm2 V−1 s−1 and highly dependent on the growth method, choice of substrate, and dopants. Although these findings have been encouraging for fundamental studies and potential applications in room-temperature oxide electronics, there still remains many open fundamental questions and challenges including the role of defects on the properties of BaSnO3 and the scattering mechanisms that limit the mobility in thin films from reaching values close to bulk mobility. These questions will be addressed in this thesis by studying thin films of BaSnO3 grown by molecular beam epitaxy. One of the challenges with the growth of BaSnO3 is the high electronegativity (low oxidation potential) of tin suggesting that stronger oxidizing conditions such as ozone or high-pressure oxygen plasma are required to achieve full oxidation of Sn. Such extreme oxidation conditions in an ultra-high vacuum molecular beam epitaxy system may lead to undesirable consequences such as oxidation of elemental sources leading to flux-instabilities, filament oxidation, and potential damage to vacuum pumps. As the first step in this direction, a new radical-based hybrid MBE approach for tin-based compounds is developed. For BaSnO3 growth, Ba is supplied through effusion from a cell, Sn using a chemical precursor (hexamethylditin – (CH3)6Sn2), and oxygen using a radio frequency plasma source. The unique aspect of our approach is that hexamethylditin forms highly reactive Sn• radicals, which facilitate the growth of phase-pure, stoichiometric films even in weak oxidizing environment such as molecular oxygen. Using this approach, synthesis of phase-pure and epitaxial BaSnO3 with scalable growth rates and layer-by- layer control over thicknesses is reported. Reflection high-energy electron diffraction is used to describe the strain relaxation behavior of BaSnO3. Various characterization techniques are employed for establishing the stoichiometric growth condition such as X-ray diffraction for lattice parameter measurements, Rutherford backscattering spec- trometry for quantification of cation (Sn:Ba) ratio, atomic force microscopy for imaging the surface morphology, electronic transport for measuring the carrier concentrations, resistivity, and electron mobility in lanthanum-doped BaSnO3 films, and time-domain thermoreflectance for determining the thermal conductivity. With the combination of these techniques, existence of a self-regulating “growth-window” is demonstrated. Through controlled La-doping in BaSnO3 films, a highest room-temperature electron mobility of 120 cm2 V−1 s−1 is achieved on a -5.12 % lattice-mismatched SrTiO3 substrate. The optimal doping range for the highest mobility is found to be 5.0 × 1019 cm−3 to 5.0 × 1020 cm−3. Mobility decreases at higher or lower doping concentrations. Temperature-dependent measurements of mobility provide insights into the scattering mechanisms limiting the mobility at different doping concentrations and temperatures. While dislocation scattering is found to be dominant at low doping regime, ionized impurity scattering plays a major role at high doping levels. At intermediate doping concentrations, both scattering mechanisms control the transport behavior. Phonon scattering accounts for the decreasing trend in mobility with increasing temperature. Building upon these findings which revealed mobility-limiting mechanisms in uniformly doped BaSnO3, the final step involves the development of modulation doping approach n BaSnO3-based heterostructures. The basic idea behind modulation doping is to sep- arate electrons from their ionized donors. Favorable band offsets in BaSnO3–SrTiO3 and BaSnO3–SrSnO3 systems are established. Taking BaSnO3–SrSnO3 as the model heterostructure, electron transfer from La-doped SrSnO3 to BaSnO3 is demonstrated, resulting in dramatic changes in the transport behavior. Results are encouraging and clearly suggest that electrons in BaSnO3 can be separated from ionized dopants. The transport, however, is still limited by dislocations and defects at the interface which should be the focus of future studies.