I will discuss results from recent studies on production of radioisotopes by muon-induced showers in neutrino detectors located deep underground. Cosmogenic radioisotopes represent one of the most significant and important classes of background for experiments on solar neutrinos. I will show how a detailed understanding of the production mechanisms of the radioisotopes can help in opening new windows of observation for low energy solar neutrinos (in particular, pep neutrinos). I will also review the status and the plans for the WARP experiment at Gran Sasso. WARP is a two-phase argon drift chamber designed for direct detection of WIMP Dark Matter. In the context, I will also draw some connections to the important role of cosmogenic background in experiments aiming at direct observation of WIMP Dark Matter.