A quantum quench is a rapid change in time of a control parameter in the hamiltonian describing a quantum, correlated many body system. The physics of this paradigmatic nonequilibrium process, which has been realized recently in the context of cold atoms, is of particular interest in quantum critical systems. In this talk I will discuss a fundamental way to characterize these processes using basic thermodynamic variables and looking at their statistics. Focusing on the statistics of the work done in a quantum quench I will first elucidate the relation between the probability distribution of the work, quantum Jarzynski equalities, and the Loschmidt echo, a quantity that emerges usually in the context of dephasing. Using this connection, I will then characterize the statistics of the work done on a quantum Ising chain by quenching locally or globally the transverse field, showing that for local quenches starting at criticality, the probability distribution of the work displays an interesting edge singularity. Ref: Alessandro Silva, Phys. Rev. Lett. 101, 120603 (2008).