With few exceptions biological tissues strongly scatter light, making high-resolution deep imaging impossible for traditional -including confocal- fluorescence microscopy. Nonlinear optical microscopy, in particular two photon-excited fluorescence microscopy, has overcome this limitation, providing large depth penetration mainly because even multiply scattered signal photons can be assigned to their origin as the result of localized nonlinear signal generation. Two-photon microscopy thus allows cellular imaging several hundred microns deep in various organs of living animals. Here we review fundamental concepts of nonlinear microscopy and discuss conditions relevant for achieving large imaging depths in intact tissue.