We review the fundamental principles and experimental implementations of multipass cells used as a platform for nonlinear optics. Embedding a nonlinear medium in a multipass cell allows for a distribution of the nonlinearity over large interaction distances, while the beam goes through multiple foci, conferring on the beam a robustness with respect to spatio-spectral coupling effects. Most of the research so far has been focused on temporal compression based on self-phase modulation, with excellent performances especially in terms of energy scaling and throughput. However, other nonlinear phenomena and functions are being increasingly investigated, such as supercontinuum generation, spectral compression, or Raman scattering. Nonlinear optics experiments in multipass cells bear some similarities with the work done in optical fibers over several decades, while allowing straightforward energy scaling potential, and unlocking engineering possibilities through the design of the cell mirrors, geometry, and nonlinear medium.