X-ray Computed Tomography (CT) is an exceptionally versatile tool for diagnosis and detection. Despite numerous technological evolutions, the underlying mechanism for CT image formation has not changed. To markedly expand beyond the current capacity of X-ray CT based on a new image formation mechanism, we introduce pair production tomography (P2T) imaging. Unlike CT, whose signals arise from attenuation of the incident photons, P2T collects coincident annihilation photons originated from the pair production interaction with high energy X-rays for tomographic reconstruction. We studied three P2T acquisition methods, including filtered back projection (FBP), time-of-flight (TOF), and scanning pencil beam (SPB). Using Monte Carlo simulation on phantom and patient data, we demonstrate three distinctly new capabilities for P2T: high linearity with the material atomic number for element mapping and soft tissue differentiation, the ability to form tomography with as few as a single heavily truncated X-ray beam, and in vivo radiotherapy treatment dose verification and monitoring. Among the three P2T acquisition methods, FBP is the least technically demanding, but its utility is limited to high radiation dose procedures such as radiotherapy treatment monitoring. Both TOF and SPB result in high signal-to-noise ratio (SNR) P2T images with a typical imaging dose. The quality of TOF relies on the time resolution of detectors. In comparison, SPB suppresses localization errors based on the known excitation path, which significantly mitigates the detector time resolution requirement.