In almost every cell type, the concentration of intracellular free calcium controls a variety of important processes, such as secretion, synaptic communication, muscular contraction, and cellular differentiation. Often, this control is exerted in a frequency-dependent manner via oscillations in the calcium concentration. Thus, over the last 15 years or so, the study of intracellular calcium dynamics has become an active research area for theoreticians and experimentalists alike. I will discuss how very simple mathematical approaches can lead to significant physiological insight into the mechanisms underlying calcium oscillations, and how these simple models can, in their turn, pose non-trivial mathematical questions.