  We give an overview of the scaling of density of quasi-particles and excess
energy (heat) for nearly adiabatic dynamics near quantum critical points
(QCPs). In particular we discuss both sudden quenches of small amplitude and
slow sweeps across the QCP. We show close connection between universal scaling
of these quantities with the scaling behavior of the fidelity susceptibility
and its generalizations. In particular we argue that the Kibble-Zurek scaling
can be easily understood using this concept. We discuss how these scalings can
be derived within the adiabatic perturbation theory and how using this approach
slow and fast quenches can be treated within the same framework. We also
describe modifications of these scalings for finite temperature quenches and
emphasize the important role of statistics of low-energy excitations. In the
end we mention some connections between adiabatic dynamics near critical points
with dynamics associated with space-time singularities in the metrics, which
naturally emerges in such areas as cosmology and string theory.
