Radio localization is a key enabling technology for situational awareness but conventional techniques based on elaborate ray-tracing approaches naturally struggle in rich scattering environments (inside rooms, metro stations, planes, vessels, . . . ). Here, we discuss a completely different approach to radio localization: instead of attempting to understand rich scattering wave propagation in terms of rays, we harness the overwhelming complexity because it assigns unique wave fingerprints to each object position. We interpret wave propagation as a physical encoder of the sought-after localization information in multiplexed measurements and detail artificial neural network (ANN) architectures suitable to decode these measurements for a single or multiple, discrete or continuous, sought-after location variable(s). Capitalizing on recent physics-driven experiments, we clarify that the proposed technique is very robust to measurement noise and capable of achieving deeply sub-wavelength localization precision. The discussed technique can be implemented with multiplexing across spatial, spectral or configurational degrees of freedom, corresponding to sensor networks, broadband measurements and RIS-programmable environments, respectively. Specifically, multiplexing across a fixed random sequence of RIS configurations enables single-frequency localization with a single node. Finally, we propose an end-to-end vision of the technique in which programmable RIS elements take the role of physical weights in a hybrid analog-digital ANN. Thereby, relevant information for the localization task can be discriminated from irrelevant information already in the measurement process, enabling substantial latency improvements.