In this talk we investigate stochastic chemical reaction networks (CRNs) with scaling methods. This approach is used to study the stability properties of the associated Markov processes, but also to investigate the transient behavior of the sample paths. It also gives insight on the impact of specific features of these networks such as their polynomial reaction rates, leading to the coexistence of multiple timescales. Some examples of CRNs are discuss to illustrate the multiple timescales involved in the decay of the norm of the state when the CRN starts from a “large” initial state. A detailed scaling analysis of an interesting CRN exhibiting a slow decrease of the norm of the state is presented.