Studies on intrinsic Josephson junctions (IJJs) of cuprate superconductors are reviewed. A system consisting of a few IJJs provides phenomena to test the Josephson phase dynamics and its interaction between adjacent IJJs within a nanometer scale, which is unique to cuprate superconductors. Quasiparticle density of states, which provides direct information on the Cooper-pair formation, is also revealed in the system. In contrast, Josephson plasma emission, which is an electromagnetic wave radiation in the sub-terahertz frequency range from an IJJ stack, arises from the synchronous phase dynamics of hundreds of IJJs coupled globally. This review summarizes a wide range of physical phenomena in IJJ systems having capacitive and inductive couplings with different nanometer and micrometer length scales, respectively.