  Estimation of parameters is a pivotal task throughout science and technology.
Quantum Cram\'{e}r-Rao bound provides a fundamental limit of precision allowed
to achieve under quantum theory. For closed quantum systems, it has been shown
how the estimation precision depends on the underlying dynamics. Here, we
propose a general formulation for metrology scenarios in open quantum systems,
aiming to relate the precision more directly to properties of the underlying
dynamics. This feature may be employed to enhance an estimation precision,
e.g., by quantum control techniques. Specifically, we derive a Cram\'{e}r-Rao
bound for a fairly large class of open system dynamics, which is governed by a
(time-dependent) dynamical semi-group map. We illustrate the utility of this
scenario through three examples.
