This paper describes a rigorous approach to radar vision. The two foundations of the approach are a theory for handling the structure and uncertainties found in radar vision and a testbed implementation of portions of that theory. The theory is novel and powerful in that it explicitly accounts for uncertainties in object modeling and electromagnetic phenomenology modeling. A key concept is that the vision problem itself is modeled as a highly structured, probabilistic, joint parameter estimation problem involving many observables and unknowns. The parameters are both discrete, such as existence or type, and continuous, such as location or shape. The problem structure involves widespread conditional decoupling of effects and allows for efficient, near-optimal algorithms for inferring world parameters from observations.