Positron Emission Tomography is a powerful medical imaging modality for investigating human and animal biochemistry and physiology. Detection of photon pairs produced by positron-electron annihilation produces tomographic projections of the spatial distribution of positron-emitting nuclei. Tomographic reconstruction methods can then be used to form volumetric images. By labelling biochemicals with positron-emitting nuclei, we can produce images of a wide variety of biochemical and physiological processes. PET is now widely used in detecting and staging cancer through imaging of glucose. In the brain, receptor and transmitter ligands have been developed to study the dopamine and other neurochemical systems. The most exciting recent development in PET is the ability to directly image gene expression through the use of PET tracer/reporter gene combinations. In humans this technique can be used, for example, to monitor the efficacy of gene therapy techniques. PET gene expression imaging is also being increasingly used to study gene expression in transgenic animals. Essential to the success of positron tomography in these diverse applications is a combination of instrumentation-design optimized for specific applications (e.g. humans vs. small animals) and image processing methods that maximize image quality when forming volumetric images from PET data. After reviewing the instrumentation and principles behind PET, I will describe statistically-based approaches to reconstructing PET images. Using a Bayesian formulation, we combine accurate physical models of the physics underlying PET systems with accurate statistical models for photon limited data collected in these systems. I will illustrate the impact of this approach on image quality through examples for clinical and animal studies. I will also describe our current work on evaluating image quality through a combination of theoretical, Monte-Carlo and human-observer studies.