Classical photography uses steady-state illumination and light sensing with focusing optics to capture scene reflectivity as images; temporal variations of the light field are not exploited. This thesis explores the use of time-varying optical illumination and time-resolved sensing along with signal modeling and computational reconstruction. Its purpose is to create new imaging modalities, and to demonstrate high-quality imaging in cases in which traditional techniques fail to even form degraded imagery. The principal contributions in this thesis are the derivation of physically-accurate signal models for the scene's response to timevarying illumination and the photodetection statistics of the sensor, and the combining of these models with computationally tractable signal recovery algorithms leading to image formation. In active optical imaging setups, we use computational time-resolved imaging to experimentally demonstrate: non line-of-sight imaging or looking around corners, in which only diffusely scattered light was used to image a hidden plane which was completely occluded from both the light source and the sensor; single-pixel 3D imaging or compressive depth acquisition, in which accurate depth maps were obtained using a single, non-spatially resolving bucket detector in combination with a spatial light modulator; and high-photon efficiency imaging including first-photon imaging, in which high-quality 3D and reflectivity images were formed using only the first detected photon at each sensor pixel despite the presence of high levels of background light.