We give a brief review of the theory of quantum universal invaxiants and their counterparts in the physics of light and particle beams. The invariants concerned are certain combinations of the second-and higher-order moments (variances) of quantum-mechanical operators, or the transverse phase-space coordinates of the paraxial beams of light or particles. They are conserved in time (or along the beam axis) independently of the concrete fbrm of the coefficients of the SchrSdinger-like equations governing the evolution of the systems, provided that the effective Hamiltonian is either a generic quadratic form of the generalized coordinatemomenta operators or a linear combination of generators of some finite-dimensional algebra (in particular, any semisimple Lie algebra). Using the phase space representation of quantum mechanics (paraxial optics) in terms of the Wigner function, we elucidate the relation of the quantmn (optical) invariants to the classical universal integral invaxiants of Poincax@ and Cartan. The specific features of Gaussian beams are discussed as examples. The concept of the universal quantum integrals of motion is introduced, and examples of the "universal invaxiant solutions" to the Schrbdinger equation, i.e., self-consistent eigenstates of the universal integrals of motion, axe given.