the $p-$eulerian polynomial $w_p(x)$ of a finite naturally labelled poset $p$ is the generating function for linear extensions of $p$ by number of descents. we will discuss some recent work related to the question of whether the coefficients of $w_p(x)$ are unimodal and whether $w_p(x)$ has real zeros. in particular we will explain the beautiful work of branden on sign-graded posets.