  This Perspective presents a comprehensive account of the dissipaton theories
developed in our group since 2014, including the physical picture of
dissipatons and the phase-space dissipaton algebra. The
dissipaton-equation-of-motion-space (DEOM-space) formulations cover the
Schr\"odinger picture, the Heisenberg picture, and further the imaginary-time
DEOM. Recently developed are also the dissipaton theories for studying
equilibrium and nonequilibrium thermodynamic mixing processes. The Jarzynski
equality and Crooks relation are accurately reproduced numerically. It is
anticipated that dissipaton theories would remain essential towards a
maturation of quantum mechanics of open systems.
