In the paper different types of bursting Ca 2þ oscillations are presented. We analyse bursting behaviour in four recent mathematical models for Ca 2þ oscillations in non-excitable cells. Separately, regular, quasi-periodic, and chaotic bursting Ca 2þ oscillations are classified into several subtypes. The classification is based on the dynamics of separated fast and slow subsystems, the so-called fast-slow burster analysis. For regular bursting Ca 2þ oscillations two types of bursting are specified: Point-Point and Point-Cycle bursting. In particular, the slow passage effect, important for the Hopf-Hopf and SubHopf-SubHopf bursting subtypes, is explained by local divergence calculated for the fast subsystem. Quasi-periodic bursting Ca 2þ oscillations can be found in only one of the four studied mathematical models and appear via a homoclinic bifurcation with a homoclinic torus structure. For chaotic bursting Ca 2þ oscillations, we found that bursting patterns resulting from the period doubling root to chaos considerably differ from those appearing via intermittency and have to be treated separately. The analysis and classification of different types of bursting Ca 2þ oscillations provides better insight into mechanisms of complex intra-and intercellular Ca 2þ signalling. This improves our understanding of several important biological phenomena in cellular signalling like complex frequency-amplitude signal encoding and synchronisation of intercellular signal transduction between coupled cells in tissue.