Quantum chaos (or wave chaos) is the study of phenomena in the quantum domain (or in other wave systems) which correspond to the classical chaos. Generic Hamiltonian systems are those with divided classical phase space: regular motion on invariant tori for some initial conditions, and chaotic motion for complementary initial conditions. Quantaly, in the semiclassical limit, we have to separate regular and chaotic eigenstates, which we do not do only conceptually, but also mathematically. Furthermore, we study the structure of chaotic eigenstates. If the quantal Heisenberg time (Planck constant divided by the average energy spacing of discrete energy spectra) is shorter than the relevant classical transport time (diffusion time, or relaxation time), we find localized chaotic eigenstates, and extended chaotic eigenstates otherwise. I shall quantify these ideas, and present also the manifestation of these phenomena in the statistical properties of the discrete energy spectra.