Polarization may be sensed by imaging modules. This is done in various engineering systems as well as in biological systems, specifically by insects and some marine species. However, polarization per pixel is usually not the direct variable of interest. Rather, polarization-related data serve as a cue for recovering task-specific scene information. How should polarization-picture post-processing (P(4)) be done for the best scene understanding? Answering this question is not only helpful for advanced engineering (computer vision), but also to prompt hypotheses as to the processing occurring within biological systems. In various important cases, the answer is found by a principled expression of scene recovery as an inverse problem. Such an expression relies directly on a physics-based model of effects in the scene. The model includes analysis that depends on the different polarization components, thus facilitating the use of these components during the inversion, in a proper, even if non-trivial, manner. We describe several examples for this approach. These include automatic removal of path radiance in haze or underwater, overcoming partial semireflections and visual reverberations; three-dimensional recovery and distance-adaptive denoising. The resulting inversion algorithms rely on signal-processing methods, such as independent component analysis, deconvolution and optimization.