We introduce and discuss photon-processing detectors and we compare them with photon-counting detectors. By estimating a relatively small number of attributes for each collected photon, photon-processing detectors may help understand and solve a fundamental theoretical problem of any imaging system based on photon-counting detectors, namely null functions. We argue that photon-processing detectors can improve task performance by estimating position, energy, and time of arrival for each collected photon. We consider a continuous-to-continuous linear operator to relate the object being imaged to the collected data, and discuss how this operator can be analyzed to derive properties of the imaging system. Finally, we derive an expression for the characteristic functional of an imaging system that produces list-mode data.