  When an isolated quantum system is driven out of equilibrium, expectation
values of general observables start oscillating in time. This article reviews
the general theory of such temporal fluctuations. We first survey some results
on the strength of such temporal fluctuations. For example temporal
fluctuations are exponentially small in the system's volume for generic systems
whereas they fall-off algebraically in integrable systems. We then concentrate
on the the so-called quench scenario where the system is driven
out-of-equilibrium under the application of a sudden perturbation. For
sufficiently small perturbations, temporal fluctuations of physical observables
can be characterized in full generality and can be used as an effective tool to
probe quantum criticality of the underlying model. In the off-critical region
the distribution becomes Gaussian. Close to criticality the distribution
becomes a universal function uniquely characterized by a single critical
exponent, that we compute explicitly. This contrasts standard equilibrium
quantum fluctuations for which the critical distribution depends on a numerable
set of critical coefficients and is known only for limited examples. The
possibility of using temporal fluctuations to determine pseudo-critical
boundaries in optical lattice experiments is further reviewed.
