In 1931, Maria Göppert-Mayer published her doctoral dissertation on the theory of two-photon quantum transitions (two-photon absorption and emission) in atoms. This report describes and analyzes the theoretical and experimental work on nonlinear optics, in particular two-photon excitation processes, that occurred between 1931 and the experimental implementation of two-photon excitation microscopy by the group of Webb in 1990. In addition to Maria Göppert-Mayer's theoretical work, the invention of the laser has a key role in the development of two-photon microscopy. Nonlinear effects were previously observed in different frequency domains (low-frequency electric and magnetic fields and magnetization), but the high electric field strength afforded by lasers was necessary to demonstrate many nonlinear effects in the optical frequency range. In 1978, the first high-resolution nonlinear microscope with depth resolution was described by the Oxford group. Sheppard and Kompfner published a study in Applied Optics describing microscopic imaging based on second-harmonic generation. In their report, they further proposed that other nonlinear optical effects, such as two-photon fluorescence, could also be applied. However, the developments in the field of nonlinear optical stalled due to a lack of a suitable laser source. This obstacle was removed with the advent of femtosecond lasers in the 1980s. In 1990, the seminal study of Denk, Strickler, and Webb on two-photon laser scanning fluorescence microscopy was published in Science. Their paper clearly demonstrated the capability of two-photon excitation microscopy for biology, and it served to convince a wide audience of scientists of the potential capability of the technique.