I will discuss compactifications of the moduli space of smooth plane curves of degree d at least 4. We will regard a plane curve as a log Fano pair $(\mathbb{P}^2,aC)$, where a is a rational number, and study the compactifications coming from K stability for general log Fano pairs. We establish a wall crossing framework to study these spaces as a varies and show that, when a is small, the moduli space coming from K stability is isomorphic to the GIT moduli space. We describe all wall crossings for degree 4, 5, and 6 plane curves and discuss the picture for general Q-Gorenstein smoothable log Fano pairs. This is joint work with Kenneth Ascher and Yuchen Liu.