I will describe recent results on model reduction for some singularly perturbed systems that arise as stochastic models of biochemical reactions. This study was initially motivated by some questions in gene expression. The process of gene expression is the sequence of chemical reactions through which genes (segments of DNA) synthesize protein. I will start with a simple gene network (consisting of a single gene, its mRNA and protein) with two distinct time scales where the network displays a negative feedback mechanism - the protein is an inhibitor for its own production. The study is carried out in the framework of the 'linear noise approximation' (also called the van Kampen approximation): one has here a singularly perturbed ODE (the reaction rate ODE of deterministic chemical kinetics) driving a singularly perturbed stochastic differential equation (SDE) which describes Gaussian fluctuations about the ODE. Working with the backward Kolmogorov equation, reduced models for the system are identified. I will also discuss extensions to more general (multiscale) chemical kinetics systems and describe a (second) application: an mRNA genetic switch. (joint work with Paul Atzberger, Mustafa Khammash)