  The laws of quantum mechanics allow to perform measurements whose precision
supersedes results predicted by classical parameter estimation theory. That is,
the precision bound imposed by the central limit theorem in the estimation of a
broad class of parameters, like atomic frequencies in spectroscopy or external
magnetic field in magnetometry, can be overcome when using quantum probes.
Environmental noise, however, generally alters the ultimate precision that can
be achieved in the estimation of an unknown parameter. This tutorial reviews
recent theoretical work aimed at obtaining general precision bounds in the
presence of an environment. We adopt a complementary approach, where we first
analyze the problem within the general framework of describing the quantum
systems in terms of quantum dynamical maps and then relate this abstract
formalism to a microscopic description of the system's dissipative time
evolution. We will show that although some forms of noise do render quantum
systems standard quantum limited, precision beyond classical bounds is still
possible in the presence of different forms of local environmental
fluctuations.
