This review deals with the physics of two-photon particle production and its applications. Two main problems are discussed first, what can one find out from the investigation of the two-photon production of hadrons and how, and second, how can the two-photon production of leptons be used? The basic method for extracting information on the 77 -* h (hadrons) transition - the ee -> eeh reaction - is discussed in detail. In particular, we discuss what information on the 77 -> h transition can be extracted from the related experiments and how it can be done. One examines which questions in hadrodynamics and photohadron interaction physics can be answered by such investigations. It is emphasized that their main peculiarity is the possibility of investigating dependence of the amplitude on the energy as well as on the masses of both colliding particles (photons). The applications of two-photon lepton production in experimental high energy physics are discussed (the form factor investigation, the search for the real part of some forward scattering amplitudes, some auxiliary problems, etc.). Applications to the search for new (hypothetical) particles are considered. A number of important differential distributions are given. Cross section estimations for different experimental set ups are obtained. A critical discussion of the equivalent photon approximation is given.