Reaction networks are mathematical models well-suited to describe the time evolution of a system of interacting molecules in an homogeneous, well-mixed volume. The stochastic model is typically used when few molecules are present, while the deterministic model is used to keep track of the changes in concentration of largely abundant reactants. In both cases, inferring dynamical properties from the easier analysis of graphical features of the network is desirable. I will show examples of results in this sense, by introducing some of the known theory on complex balanced and absolute concentration robustness models. I will then proceed to show how the long-term behavior of the stochastic and deterministic models can sometimes be similar, and sometimes systematically and substantially differ.