Wavefront sensing is a fundamental problem in applied optics. Wavefront sensors that work in a deterministic manner are of particular interest. Initialized with a unified theory for classical wavefront sensors, this dissertation discusses relevant properties of wavefront sensor designs. Based on which, a new wavefront sensor, termed Coded Wavefront Sensor, is proposed to leverage the advantages of the analysis, especially the lateral wavefront resolution. A prototype was built to demonstrate this new wavefront sensor. Given that, two specific applications are demonstrated: megapixel adaptive optics and simultaneous intensity and phase imaging. Combined with a spatial light modulator, a hardware deconvolution approach is demonstrated for computational cameras via a high resolution adaptive optics system. By simply switching the normal image sensor with the proposed one, as well as slight change of illumination, a bright field microscope can be configured to a simultaneous intensity and phase microscope. These show the broad application range of the proposed computational wavefront sensing approach. Lastly, this dissertation proposes the idea of differentiable optics for wavefront engineering and lens metrology. By making use of automatic differentiation, a physically-correct differentiable ray tracing engine is built, with its potentials being illustrated via several challenging applications in optical design and metrology.