  A survey of the probabilistic approaches to quantum dynamical semigroups with
unbounded generators is given. An emphasis is made upon recent advances in the
structural theory of covariant Markovian master equations. The relations with
the classical Levy-Khinchin formula are elucidated. As an example, a complete
characterizations of the Galilean covariant irreversible quantum Markovian
evolutions is given in terms of the corresponding quantum master and Langevin
equations. Important topics for future investigation are outlined.
