For centuries, traditional optical instruments have relied on the gradual accumulation of phase through bulky, refractive media, and were constrained by the limits of naturally occurring material properties. Recently, optical metasurfaces – flat nanostructured elements with extraordinary electromagnetic properties – emerged as an alternative that offers new optical functionalities. This dissertation addresses a new branch of all-dielectric metasurfaces and advances it with design, fabrication, and characterization of metasurfaces that combine several complex optical functionalities into a single device. The primary objective of this work is to advance the functionality, versatility, and efficiency of metasurfaces by focusing on three primary component classes: beam splitters, holograms, and polarization analyzers. To achieve this, the entire workflow integrating numerical methods, including finite-difference time-domain (FDTD) simulations and rigorous coupled-wave analysis (RCWA), with advanced optimization techniques such as topology optimization and parametric inverse design, was established. To ground this inverse design in real-world fabrication conditions, the optimization algorithm was supported by a meta-atom library experimentally acquired via coherence-controlled holographic microscopy (CCHM). The designed devices were subsequently fabricated using electron-beam lithography paired with atomic layer deposition or cryogenic deep reactive ion etching, and characterized using scanning electron microscopy and custom-built optical characterization setups. Computational and experimental efforts culminated in several key advancements. First, a high-purity circular polarization beam splitter based on the Pancharatnam-Berry phase was realized to separate and deflect right- and left-handed circular polarization states for an in-house-built infrared digital holographic microscope. Second, a free-form topology-optimized outcoupler engineered for thermo-radiative diodes demonstrated a light extraction efficiency enhancement of over 40% compared to a bare substrate. Third, to overcome geometric distortions in wide-angle holographic projections, a novel k-space image correction workflow and a real-space parametric inverse design algorithm were developed, facilitating distortion-free, polarization-multiplexed holograms. Finally, an inverse-designed metasurface that merges full-Stokes polarimetric capabilities with a Shack-Hartmann wavefront detector fabricated with high-aspect-ratio TiO₂ nanostructures was presented. Taken together, these results demonstrate that combining computational inverse design with advanced nanofabrication techniques enables a new generation of highly efficient, versatile, flat meta-optics capable of replacing bulky multi-component classical systems.