Astrocytes are cells of the brain that have recently emerged as key regulators of signal transmission, taking part in higher brain functions such as memory and learning. Astrocytes communicate with neighboring cells with changes in intracellular calcium concentration: Ca2+ signals. Most of these signals occur at the nanoscale, hindering their study in live tissue, so that computational approaches are essential to gain insights into their dynamics. To take into account the complex morphology of astrocytes and the stochasticity of reactions occuring in the resulting nanoscopic compartments, we have developed reaction-diffusion particle-based and voxel-based models of astrocyte Ca2+ dynamics. Our simulations revealed mechanisms by which spatial factors such as the clustering of Ca2+ channels, Ca2+ buffering, ER shape and distribution influence the spatio-temporal properties of Ca2+ signals. Astrocytes and their Ca2+ signals are essential to the functioning of the nervous system and are altered in most brain disorders. As research has for long focused on treating neurons, little is known about astrocyte (patho-)physiology and better characterizing astrocyte function might lead to the discovery of new treatments for the diseased brain.