The explicit descriptions of low degree K3 surfaces lead to natural compactifications coming from geometric invariant theory (GIT) and Hodge theory. The relationship between these compactifications for degree two K3 surfaces was studied by Shah and Looijenga, and revisited by Laza and O’Grady, who also provided a conjectural description for the case of degree four K3 surfaces. I will discuss these results, as well as a verification of this conjectural picture using tools from K-moduli. This is joint work with Kristin DeVleming and Yuchen Liu.