Changes in cellular Ca2+ concentration control a wide range of physiological processes, from the subsecond release of synaptic neurotransmitters, to the regulation of gene expression over months or years. Ca2+ can also trigger cell death through both apoptosis and necrosis, and so the regulation of cellular Ca2+ concentration must be tightly controlled through the concerted action of pumps, channels and buffers that transport Ca2+ into and out of the cell cytoplasm. A hallmark of cellular Ca2+ signalling is its spatiotemporal complexity: stimulation of cells by a hormone or neurotransmitter leads to oscillations in cytoplasmic Ca2+ concentration that can vary markedly in time course, amplitude, frequency, and spatial range. In this chapter we review some of the biological roles of Ca2+, the experimental characterisation of complex dynamic changes in Ca2+ concentration, and attempts to explain this complexity using computational models. We consider the 'toolkit' of cellular proteins which influence Ca2+ concentrarion, describe mechanistic models of key elements of the toolkit, and fit these into the framework of whole cell models of Ca2+ oscillations and waves. Finally, we will touch on recent efforts to use stochastic modelling to elucidate elementary Ca2+ signal events, and how these may evolve into global signals.