  Gamma-positivity is an elementary property that polynomials with symmetric
coefficients may have, which directly implies their unimodality. The idea
behind it stems from work of Foata, Sch\"utzenberger and Strehl on the Eulerian
polynomials; it was revived independently by Br\"and\'en and Gal in the course
of their study of poset Eulerian polynomials and face enumeration of flag
simplicial spheres, respectively, and has found numerous applications since
then. This paper surveys some of the main results and open problems on
gamma-positivity, appearing in various combinatorial or geometric contexts, as
well as some of the diverse methods that have been used to prove it.
