  Dynamical semigroups have become the key structure for describing open system
dynamics in all of physics. Bounded generators are known to be of a standard
form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often
used also in the unbounded case, but rather little is known about the general
form of unbounded generators. In this paper we first give a precise description
of the standard form in the unbounded case, emphasizing intuition, and
collecting and even proving the basic results around it. We also give a
cautionary example showing that the standard form must not be read too naively.
Further examples are given of semigroups, which appear to be probability
preserving to first order, but are not for finite times. Based on these, we
construct examples of generators which are not of standard form.
