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HIF-1 (Hypoxia Inducible Factor-1) is an oxygen-regulated transcription factor that mediates the intracellular response to hypoxia in human cells, targeting specific genes that promote cell survival by inducing processes such as angiogenesis and glycolysis. The HIF-1 signalling pathway has been of considerable interest due to its role in mammalian development and in particular several pathologies such as ischemia and cancer. Low cellular oxygen levels are found in cancer due to the rapid proliferation of tumour cells distant to blood vessels (forming a hypoxic core) and the typically irregular vasculature is unable to properly perfuse the tumour. In the Centre for Cell Imaging at the University of Liverpool, time lapsed imaging in an oxygen-controlled environment has captured the transient dynamics of the oxygen regulated subunit of HIF-1, HIF-1α, and revealed heterogeneity between individual cells. The essential characteristics of this data are modelled with a system of differential equations describing the feedback inhibition between HIF-1α and the pathway’s effective oxygen sensors. This novel model was formulated by employing a minimalist approach initially, allowing us to use the rich variety of single-cell data to determine the structure of the feedback loop between two key pathway components. Once the central regulatory motif was identified, the model was expanded to include more complexity, including experimental measurements for model parameter values and additional system components. Oxygen plays an especially important role in the early stages of tumour formation. Measurements of oxygen within cells have been recorded in cultured spheres of neuroblastoma cells at different atmospheric conditions. This data is representative of the early development stages of an avascular tumour and a spatial oxygen-diffusion model was coupled with the single-cell HIF-1α model to describe the dynamics of HIF-1α across a developing tumour. This coupled model is used to study HIF-1α dynamics in the context of various oxygen-dependent cellular functions such as cell-cycle progression and apoptosis by integrating with modifications of published mathematical models.