  In this article, we review the theory of Gaussian multiplicative chaos
initially introduced by Kahane's seminal work in 1985. Though this beautiful
paper faded from memory until recently, it already contains ideas and results
that are nowadays under active investigation, like the construction of the
Liouville measure in 2d-Liouville quantum gravity or thick points of the
Gaussian Free Field. Also, we mention important extensions and generalizations
of this theory that have emerged ever since and discuss a whole family of
applications, ranging from finance, through the Kolmogorov-Obukhov model of
turbulence to 2d-Liouville quantum gravity. This review also includes new
results like the convergence of discretized Liouville measures on isoradial
graphs (thus including the triangle and square lattices) towards the continuous
Liouville measures (in the subcritical and critical case) or multifractal
analysis of the measures in all dimensions.
