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