Gene regulatory networks (GRNs) lie at the core of intracellular signal transduction and can be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. One of the key players in GRNs is a class of proteins called transcription factors. In response to a variety of biological signals, transcription factors modify the transcription rate of genes, allowing cells to produce the proteins they need at the appropriate times and in the appropriate quantities. It is now well established that GRNs contain a small set of recurring regulation patterns, which are commonly referred to as network motifs. The correct localisation of transcription factors is vitally important for the proper functioning of many intracellular signalling pathways. Experimental data have shown that many pathways exhibit oscillations in concentrations of the molecules involved, both temporally and spatially. Negative feedback loops are important components of these oscillations, providing fine regulation for the factors involved. Using partial differential equation models, new information can be gained about the precise spatio-temporal dynamics of mRNA and proteins, including transport across the nuclear membrane and active transport along microtubules. The ability to determine spatial localisation of proteins within a cell is likely to yield fresh insight into a range of cellular diseases such as diabetes and cancer.