Cuprate superconductors have a layered crystal structure consisting of some nearby \(\mathrm{CuO}_2\) sheets which are separated from the next group of \(\mathrm{CuO}_2\) sheets by blocking layers. Cooper pairs form in the \(\mathrm{CuO}_2\) sheets. For the most anisotropic compounds such as \(\mathrm{Bi}_{2}\mathrm{Sr}_{2}\mathrm{CaCu}_{2}\mathrm{O}_8\) current-flow across the blocking layer occurs via tunneling. The interlayer supercurrent is of the Josephson type and, thus, a single crystal forms a natural stack of Josephson junctions. Intrinsic Josephson junctions (IJJs) have been investigated for more than two decades. The research, on the one hand, provided information about many details of the interlayer transport of Josephson-coupled layered superconductors and, on the other hand, showed that IJJ stacks can be used to probe the layered superconductor “from inside”, or to generate electromagnetic radiation in the terahertz regime. This chapter introduces into the physics of IJJs and reviews part of the research achievements, including fabrication methods, theoretical and experimental results on Josephson vortex dynamics, interlayer tunneling spectroscopy, and the generation of terahertz radiation.