The New Physics sensitivity of the s ---> d gamma transition and its accessibility through hadronic processes are thoroughly investigated. Firstly, the Standard Model predictions for the direct CP-violating observables in radiative K decays are systematically improved. Besides, the magnetic contribution to epsilon prime is estimated and found subleading, even in the presence of New Physics, and a new strategy to resolve its electroweak versus QCD penguin fraction is identified. Secondly, the signatures of a series of New Physics scenarios, characterized as model-independently as possible in terms of their underlying dynamics, are investigated by combining the information from all the FCNC transitions in the s ---> d sector.