A quartic del Pezzo surface $X$ is an intersection of two degree $2$ hypersurfaces in ${\mathbb{P}}^4$. So rational points on $X$ correspond to solutions of a pair of homogeneous quadratic equations in $5$ variables. I will discuss joint work with R. Das, B. Lehmann, and S. Tanimoto, using topological methods to determine statistics of rational points on $X$ (over the function field ${\mathbb{F}}_q(t)$)