Nonlinear optics is present in our daily life with many applications, e.g. light sources for microsurgery or green laser pointer. All of them use bulk materials such as glass fibres or crystals. Generating nonlinear effects from materials at the nanoscale can expand the applications to biology as imaging markers or sensors, and to optoelectronic integrated devices. However, the nonlinear emission efficiency of nanostructures is low due to their small volumes. In our work, we show strategies to enhance the second harmonic generation (SHG) at the nanoscale with the goal of developing nonlinear photonics devices for a broad spectral range. So far, the SHG from metallic and semiconductor nanostructures as gold or gallium arsenide has been successfully shown. However, the application range of these materials is generally limited to the visible-near-infrared range by their high absorption. We use metal oxides such as barium titanate (BTO) and lithium niobate (LNO) as an alternative platform for nanoscale nonlinear photonics in a broad spectral range. Both BTO and LNO are noncentrosymmetric materials with high refractive index and high energy band gaps, transparent down to the near-ultraviolet range. We demonstrate linear Mie resonances in BTO and LNO nanostructures, such as nanospheres or nanocubes. Further, we show that these resonances enhance the SHG emission from the nanostructures. We also perform simulations to understand the underlying mechanism of this enhancement. Finally, we explore fabrication methods for BTO and LNO nanostructures that will allow the controlled integration of BTO and LNO nanostructures for nonlinear metasurfaces.