Exploiting nonclassical states of light allows new imaging and sensing approaches. In particular, nonlinear interferometers enable quantum sensing with undetected light. Here, based on the effect of induced coherence, samples can be probed with light that is not detected at all. Instead, its quantum-correlated partner light is recorded and yields the information of the sample, although it never interacted with it. The talk will outline the fundamental concept, recent progress, limits, and perspectives for biomedical applications of nonlinear interferometers.