Here, we discuss the growth of epitaxial thin films of Cd3As2, a 3D Dirac semimetal, by molecular beam epitaxy. We report on their structure, magnetotansport properties, and field gating experiments using high-k dielectrics. The films are shown to grow in the low-temperature, vacancy ordered, tetragonal Dirac semimetal phase. Extremely high room temperature mobilities (~20,000 cm2/Vs) are achieved in epitaxial layers on III-V substrates. Unusual transport characteristics are observed, such as a negative longitudinal magnetoresistance, i.e., when the magnetic field is applied parallel to the direction of electric current. We vary the film parameters and study their influence on the magnetotransport to distinguish between ‘classical’ phenomena and effects originating from the unique electronic structure.