We introduce the concept of all-anisotropic spheroidal photonic antennas, where the nanoantenna is formed by a uniaxial anisotropic crystal, and study their modeling and optimization. For this purpose, we develop, for the first time, a rigorous theory for the electromagnetic (EM) scattering by anisotropic spheroids, using a full-wave method which features spheroidal eigenvectors with a set of discrete wavenumbers for the expansion of the fields in the region of anisotropy. We fully validate our theory by comparisons with the commercial HFSS software, as well as with a general purpose discrete dipole approximation method. Our implementation turns out to be fast, and serves as an efficient tool for modeling the resonant properties of spheroidal photonic antennas. In this context, we show that geometrical tailoring, by employing high-aspect ratio prolate and oblate spheroids, allows for optimizing the nanoantenna and achieving maximal forward-to-back scattering or maximal forward-scattering with reduced back-scattering. In addition, we demonstrate how the use of anisotropic materials enables us to set this optimum state at smaller wavelengths, even close to ultraviolet (UV), as compared to isotropic dielectrics, and we reveal the key role of the incident field's polarization in achieving optimized operation for both prolate and oblate configurations.