The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system or an equivalent system. In this talk, we will survey recent results on the mixed volume of chemical reaction networks, including related results using Newton-Okounkov bodies. We will conclude the talk by showing that for partionable networks computing the mixed volume is equivalent to finding the volume of a single mixed cell that is the translate of a parallelotope. We highlight this theorem by giving a formula for the mixed volume of species-overlapping networks. This is based on joint work with Jane Coons and Mark Curiel.