  The phenomenon of frequency and phase synchronization in stochastic systems
requires a revision of concepts originally phrased in the context of purely
deterministic systems. Various definitions of an instantaneous phase are
presented and compared with each other with special attention payed to their
robustness with respect to noise. We review the results of an analytic approach
describing noise-induced phase synchronization in a thermal two-state system.
In this context exact expressions for the mean frequency and the phase
diffusivity are obtained that together determine the average length of locking
episodes. A recently proposed method to quantify frequency synchronization in
noisy potential systems is presented and exemplified by applying it to the
periodically driven noisy harmonic oscillator. Since this method is based on a
threshold crossing rate pioneered by S.O. Rice the related phase velocity is
termed Rice frequency. Finally, we discuss the relation between the phenomenon
of stochastic resonance and noise-enhanced phase coherence by applying the
developed concepts to the periodically driven bistable Kramers oscillator.
