In this review article, we discuss the current state of computational modelling of the nuclear factor-kappa B (NF-κB) signalling pathway. NF-κB is a transcription factor, which is ubiquitous within cells and controls a number of immune responses, including inflammation and apoptosis. The NF-κB signalling pathway is tightly regulated, commencing with activation at the cell membrane, signal transduction through various components within the cytoplasm, translocation of NF-κB into the nucleus and, finally, the transcription of various genes relating to the innate and adaptive immune responses. There have been a number of computational (mathematical) models developed of the signalling pathway over the past decade. This review describes how these approaches have helped advance our understanding of NF-κB control.