  We consider a two-level quantum system (qubit) which is continuously measured
by a detector. The information provided by the detector is taken into account
to describe the evolution during a particular realization of measurement
process. We discuss the Bayesian formalism for such ``selective'' evolution of
an individual qubit and apply it to several solid-state setups. In particular,
we show how to suppress the qubit decoherence using continuous measurement and
the feedback loop.
