After defending his thesis in 1984 under the direction of Albert Libchaber as a preparatory associate at the École normale supérieure, Stephan Fauve was successively Professor at the École normale supérieure de Lyon (1987–1997), then at the ENS in Paris since 1997.

His thesis work focused on the study of various scenarios of transition to chaos, in particular the measurement of critical exponents associated with the cascade of period doubling.

[3] He was one of the founders of the physics laboratory of ENS-Lyon, initiating there the study of various research fields, such as dissipative structures generated by instability,[4] granular media,[5][6] sound propagation in complex media (effect of liquid-vapour transition on sound velocity and absorption in two-phase media),[7] sound-vorticity interaction and its application to the detection of intermittent vortex structures in turbulence,[8] the study of surface waves, which led to the first observation of a hydrodynamic quasi-crystalline pattern [9][10] and wave turbulence.

[11][12] He initiated the VKS (von Karman Sodium) collaboration by proposing an experiment on the dynamo effect that led to the first laboratory observation of magnetic field reversal,[13][14] with many similarities to the reversals of the Earth's magnetic field.

[15] He is currently interested in the statistical properties of large scales in turbulence[16][17][18] and in modelling the quasi-biennial oscillation laboratory, i. e. the quasi-periodic wind reversals in the equatorial stratosphere.