  Brascamp-Lieb inequalities have been important in analysis, mathematical
physics and neighboring areas. Recently, these inequalities have had a deep
influence on Fourier analysis and, in particular, on Fourier restriction
theory. In this article we motivate and explain this connection. A lot of our
examples are taken from a rapidly developing subarea called "decoupling". It is
the author's hope that this article will be accessible to graduate students in
fields broadly related to analysis.
