since the seminal work of yudovich in 1963, it has been known that for a given uniformly bounded and compactly supported initial vorticity profile, there exists a unique global solution to the 2d incompressible euler equation. a special class of yudovich solutions are so-called vortex patch solutions where the vorticity profile is the characteristic function of an (evolving) bounded set in $\mathbb{r}^2.$ in 1993 chemin and bertozzi-constantin proved that sufficiently high regularity of the boundary is propagated for all time. since then, there have been numerous numerical and rigorous works on understanding the long-time dynamics of smooth vortex patches as well as the short time dynamics of vortex patches with corners. in this work, we consider two regimes; one where we prove well-posedness and the other where we prove ill-posedness. first, for vortex patches with corners enjoying a certain symmetry property at the corners, we prove global propagation of the corners; we also give examples where these vortex patches cusp in infinite time. second, we prove that vortex patches with a single corner (which do not satisfy the symmetry condition) immediately cease to have a corner. this is joint work with i. jeong.