  Ehrhart theory is the study of sequences recording the number of integer
points in non-negative integral dilates of rational polytopes. For a given
lattice polytope, this sequence is encoded in a finite vector called the
Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of
mathematics, including commutative algebra and enumerative combinatorics. In
this survey we discuss what is known about unimodality for Ehrhart
$h^*$-vectors and highlight open questions and problems.
