Time series relating to gene expression are now routinely measured in various important biological experiments such as microarrays, nanostring, etc as well as experiments based on bioluminescent imaging. One of the most important aim is to gain an understanding of the transcriptional regulation of genes, i.e. what determines their activation. A natural model is to assume that gene activation is a constant rate birth process but that the rate may change to different levels at unknown time points leading to the piecewise linear “switch� model. Statistical inference for such a model poses interesting and challenging problems, in particular since experiments can only measure events downstream whereas the processes of interest remain unobserved. We will give an overview of our experience with fitting such switch models to real data where, depending on the type of experiment, our assumptions range from stochastic differential equations to the use of ordinary differential equations, along with realistic stochastic formulations of the measurement processes. We will also present further results on extending this nonlinear approach to the multivariate case of identifying networks of interacting genes. Here we find that the concept of “thresholding� constitutes a simple yet realistic and very effective modelling device to help identifying network connections. Joint work with Dafyd Jenkins, Kirsty Hey, George Minas and David Rand.