The aim of this article is to review the basic principles of two-photon excitation fluorescence (2PEF) microscopy and to compare the advantages and disadvantages of 2PEF imaging to other microscopy methodologies. 2PEF imaging is a nonlinear approach that generates images of optical sections and that is particularly well suited for deep-tissue and in vivo imaging of live animals. The nonlinear excitation used for 2PEF offers the advantage, too, of being able to generate contrast from second or third harmonic generation as well as coherent anti-Stokes Raman scattering. We also review the recent use of nonlinear excitation to provide image resolution beyond the diffraction limit and discuss the progress in non-scanning (planar) 2PEF microscopy, an approach that holds great potential for large-scale quantitative imaging and plate reading, e.g., in screening applications.