The spatiotemporal diversity of Ca2+ signals enables them to mediate diverse functions inside the same cell; this diversity arises in part from the position, arrangement, and communication between Ca2+ permeable channels. The work presented in this thesis describes various approaches for determining how these complex Ca2+ signals are generated. The first part of this dissertation describes the construction of two types of microscopes which enhance spatiotemporal resolution of Ca2+ signals. The spinning-spot shadowless total internal reflection fluorescence microscopy (chapter 2) provides enhanced shadow-free imaging of Ca2+ signals arising near the plasma membrane. A simplified lattice light-sheet microscope (chapter 3) enables high spatial resolution and 3D visualization of Ca2+ signals throughout the cell. This dissertation also describes new analytic techniques for understanding local Ca2+ signals. Chapter 4 describes a new set of algorithms and software for detecting and analyzing of local calcium signals. Chapter 5 details the precision with which the location of channels underlying local Ca2+ signals can be determined. In the next two chapters, these techniques are applied to study signaling pathways involving two important Ca2+ permeable channels. In chapter 6, Ca2+ signals generated by the inositol trisphosphate receptor (IP3R) are used to infer the diffusion coefficient of its agonist, IP3, leading to the conclusion that IP3 is a local, rather than global, messenger. Chapter 7 details work which shows that the mechanosensitive Ca2+ channel Piezo1 diffuses in the plasma membrane and that its activity is enriched in regions where cells generate mechanical traction forces.