  Cross-ratio degrees count configurations of points $z_1,\ldots, z_n \in
\mathbb{P}^1$ satisfying $n - 3$ cross-ratio constraints, up to isomorphism.
These numbers arise in multiple contexts in algebraic and tropical geometry,
and may be viewed as combinatorial invariants of certain hypergraphs. We prove
an upper bound on cross-ratio degrees in terms of the theory of perfect
matchings on bipartite graphs. We also discuss several of the many perspectives
on cross-ratio degrees -- including a connection to Gromov-Witten theory -- and
give many example computations.
