Dynamical phase t ransitions can occur in isolated quantum systems t hat are brought out of equilibrium by either a sud den or a gradual change of their parameters. Theor etical examples range from the behaviour of the O( N) model as well as spin-models with long range in teractions both showing dynamical criticality in t heir prethermal steady-states. In this talk I will start by discussing the characterization of such dynamical phase transitions based on the statistic s of produced excitations. I will also discuss the role of fluctuations as well as on the difference s between sudden and gradual changes of the system parameters. Finally\, I will discuss the emergenc e of zeroes in the Loschmidt amplitude attempting to elucidate their physical meaning in connection with the dynamical transitions above. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR