1. Introduction 982. Historical background of two-photon effects 992.1 2PE 1002.2 Harmonic generation 1002.3 Fluorescence correlation spectroscopy 1003. Basic principles of two-photon excitation of fluorescent molecules and implications for microscopy and spectroscopy 1013.1 General considerations 1013.2 Fluorescence intensity under the 2PE condition 1033.3 Optical consequences of 2PE 1043.4 Saturation effects in 2PE 1083.5 Fluorescence correlation spectroscopy 1093.5.1 Autocorrelation analysis 1103.5.2 Photon-counting histogram analysis 1124. Two-photon-excited probes 1155. Design considerations for a 2PE fluorescence microscope 1195.1 General aspects 1195.2 Descanned and non-descanned 2PE imaging 1215.3 Lens objectives and pulse broadening 1225.4 Laser sources 1255.5 Example of a practical realization 1276. Applications 1346.1 Biological applications of 2PE 1346.1.1 Brain images 1346.1.2 Applications on the kidney 1396.1.3 Mammalian embryos 1396.1.4 Applications to immuno-response 1416.1.5 Myocytes 1416.1.6 Retina 1426.1.7 DNA imaging 1436.1.8 FISH applications 1446.2 2PE imaging of single molecules 1446.3 FCS applications 1486.4 Signals from nonlinear interactions 1517. Conclusions 1538. Acknowledgements 1549. References 155This review is concerned with two-photon excited fluorescence microscopy (2PE) and related techniques, which are probably the most important advance in optical microscopy of biological specimens since the introduction of confocal imaging. The advent of 2PE on the scene allowed the design and performance of many unimaginable biological studies from the single cell to the tissue level, and even to whole animals, at a resolution ranging from the classical hundreds of nanometres to the single molecule size. Moreover, 2PE enabled long-term imaging of in vivo biological specimens, image generation from deeper tissue depth, and higher signal-to-noise images compared to wide-field and confocal schemes. However, due to the fact that up to this time 2PE can only be considered to be in its infancy, the advantages over other techniques are still being evaluated. Here, after a brief historical introduction, we focus on the basic principles of 2PE including fluorescence correlation spectroscopy. The major advantages and drawbacks of 2PE-based experimental approaches are discussed and compared to the conventional single-photon excitation cases. In particular we deal with the fluorescence brightness of most used dyes and proteins under 2PE conditions, on the optical consequences of 2PE, and the saturation effects in 2PE that mostly limit the fluorescence output. A complete section is devoted to the discussion of 2PE of fluorescent probes. We then offer a description of the central experimental issues, namely: choice of microscope objectives, two-photon excitable dyes and fluorescent proteins, choice of laser sources, and effect of the optics on 2PE sensitivity. An inevitably partial, but vast, overview of the applications and a large and up-to-date bibliography terminate the review. As a conclusive comment, we believe that 2PE and related techniques can be considered as a mainstay of the modern biophysical research milieu and a bright perspective in optical microscopy.