  Dissipation, the irreversible loss of energy and coherence, from a
microsystem, is the result of coupling to a much larger macrosystem (or
reservoir) which is so large that one has no chance of keeping track of all of
its degrees of freedom. The microsystem evolution is then described by tracing
over the reservoir states, resulting in an irreversible decay as excitation
leaks out of the initially excited microsystems into the outer reservoir
environment. Earlier treatments of this dissipation described an ensemble of
microsystems using density matrices, either in Schroedinger picture with Master
equations, or in Heisenberg picture with Langevin equations. The development of
experimental techniques to study single quantum systems (for example single
trapped ions, or cavity radiation field modes) has stimulated the construction
of theoretical methods to describe individual realizations conditioned on a
particular observation record of the decay channel, in the environment. These
methods, variously described as Quantum Jump, Monte Carlo Wavefunction and
Quantum Trajectory methods are the subject of this review article. We discuss
their derivation, apply them to a number of current problems in quantum optics
and relate them to ensemble descriptions.
