The last decade witnessed a surge in applications of all-dielectric metasurfaces. Compared to traditional plasmonic materials, low-loss, high-refractive-index dielectric materials can generate strong local electric field enhancement while maintaining low optical absorption, thus providing new possibilities in various applications, such as imaging, nonlinear generation, and biosensing. In this thesis, we explore the potential of all-dielectric metasurfaces in two aspects. In the first part of this thesis, we demonstrate two novel nonlinear all-dielectric metasurface designs in the vacuum ultraviolet (VUV) region: a titanium dioxide (TiO2) metasurface that provides enhanced third harmonic generation at 185 nm by an anapole resonance near the fundamental wavelength of 555 nm, and an ultracompact zinc oxide (ZnO) metalens that effectively converts a 394-nm wave into converging 197-nm light via second harmonic generation. In the second part of the thesis, we introduce a new automated nanodevice design (inverse design) platform based on the discrete dipole approximation method (DDA) and optimization theories. With given performance metrics, this computational platform is capable of efficiently searching for optimal nanodevice geometries without intensive human labor, thus illustrating a promising strategy for designing large-scale, multifunctional all-dielectric metasurfaces.