Astrocytes are predominant glial cells in the central nervous system, which are essential for the formation of synapses, participate to the blood-brain barrier and maintain the metabolic, ionic and neurotransmitter homeostasis. Recently, astrocytes have emerged as key elements of information processing in the central nervous system. Astrocytes can contact neurons at synapses and modulate neuronal communication via the release of gliotransmitters and the uptake of neurotransmitters. The use of super-resolution microscopy and highly sensitive genetically encoded Ca2+ indicators (GECIs) has revealed a striking spatiotemporal diversity of Ca2+ signals in astrocytes. Most astrocytic signals occur in processes, which are the sites of neuron-astrocyte communication. Those processes are too fine to be resolved by conventional light microscopy so that super-resolution microscopy and computational modeling remain the only methodologies to study those compartments. The work presented in this thesis aims at investigating the effect of spatial properties (as e.g cellular geometry, molecular distributions and diffusion) on Ca2+ signals in those processes, which are deemed essential in such small volumes. Historically, Ca2+ signals were modeled with deterministic well-mixed approaches, which enabled the study of Ca2+ signals in astrocytic networks or whole-cell events. Those methods however ignore the stochasticity inherent to molecular interactions as well as diffusion effects, which both play important roles in small volumes. In this thesis, we present the spatially-extended stochastic model that we have developed in order to investigate Ca2+ signals in fine astrocytic processes. This work was performed in collaboration with experimentalists that performed electron as well as super-resolution microscopy. The model was validated against experimental data. Simulations of the model suggest that (1) molecular diffusion, strongly influenced by the concentration and kinetics of endogenous and exogenous buffers, (2) intracellular spatial organization of molecules, notably the co-clustering of Ca2+ channels, (3) ER geometry and localization within the cell, (4) cellular geometry strongly influence Ca2+ dynamics and can be responsible for the striking diversity of astrocytic Ca2+ signals. This work contributes to a better understanding of astrocyte Ca2+ signals, a prerequisite for understanding neuron-astrocyte communication and its influence on brain function.