  This work reviews deterministic and diffusion approximations of the
stochastic chemical reaction networks and explains their applications. We
discuss the added value the diffusion approximation provides for systems with
different phenomena, such as a deficiency and a bistability. It is advocated
that the diffusion approximation can be considered as an alternative
theoretical approach to study the reaction networks rather than a simulation
shortcut. We discuss two examples in which the diffusion approximation is able
to catch qualitative properties of reaction networks that the deterministic
model misses. We provide an explicit construction of the original process and
the diffusion approximation such that the distance between their trajectories
is controlled and demonstrate this construction for the examples. We also
discuss the limitations and potential directions of the developments.
