Computational cameras with sensor hardware co-designed with computer vision and graphics algorithms are an exciting recent trend in visual computing. In particular, most of these new cameras capture the plenoptic function of light, a multidimensional function of radiance for light rays in a scene. Such plenoptic information can be used for a variety of tasks including depth estimation, novel view synthesis, and inferring physical properties of a scene that the light interacts with. In this thesis, we present multimodal plenoptic imaging, the simultaenous capture of multiple plenoptic dimensions, using Angle Sensitive Pixels (ASP), custom CMOS image sensors with embedded per-pixel diffraction gratings. We extend ASP models for plenoptic image capture, and showcase several computer vision and computational imaging applications. First, we show how high resolution 4D light fields can be recovered from ASP images, using both a dictionary-based machine learning method as well as deep learning. We then extend ASP imaging to include the effects of polarization, and use this new information to image stress-induced birefringence and remove specular highlights from light field depth mapping. We explore the potential for ASPs performing time-of-flight imaging, and introduce the depth field, a combined representation of time-of-flight depth with plenoptic spatio-angular coordinates, which is used for applications in robust depth estimation. Finally, we leverage ASP optical edge filtering to be a low power front end for an embedded deep learning imaging system. We also present two technical appendices: a study of using deep learning with energy-efficient binary gradient cameras, and a design flow to enable agile hardware design for computational image sensors in the future.