Offset information is commonly available after using ray-based imaging, however the ray approximations can fail to produce an accurate image or representation of subsurface acoustic velocities in complex geology. Wave-equation imaging and velocity analysis provides a more accurate representation of the physical propagation of wavefronts, and extending the computation to the common-offset domain adds a new dimension of freedom for inversion, provides a wide aperture of illumination, and can be parameterized to avoid cycle skipping. Here, I develop common-offset reverse time migration (CORTM), a wave-equation based imaging method which splits the input data into common-offset bins prior to migration, and then extend it to least-squares migration in the common-offset domain (COLSM), an iterative inversion which produces image gathers that are closer to predicting recorded data than CORTM. With an appropriate number of offset bins, COLSM can be parameterized to avoid cycle skipping within an offset gather, increase convergence rates, amplitude fidelity and resolution. Maintaining execution in the common-offset domain additionally opens up avenues for commonly utilized offset-based processing post-migraiton. I also extend wave-equation based migration velocity analysis (WEMVA), an iterative method has been used succesfully to provide low-frequency starting models for full waveform inversion (FWI), to the common-offset domain by minimizing an image residual from either CORTM or COLSM offset images. COLSM's increased amplitude fidelity over CORTM helps to ensure that the image residual is largely a function of moveout instead of errors in amplitude, which increases the likelihood of converging to a global minimum in a long-wavelength update. Division into sufficiently small offset bins can circumvent the requirement to start from an accurate starting model and also avoid cycle-skipping and associated local minima. Lastly, I show how it is possible to approximate the tomographic operator used to create a long-wavelength update in COWEMVA by using CORTM. The following chapters detail the results of and the theory and methodology used to apply CORTM, COLSM and COWEMVA with and without the tomographic approximation to several synthetic models and one field data set.