Light cone spreading of correlations and entanglement is a key feature of the non-equilibrium dynamics of many-body quantum systems. First proposed theoretically, it has been experimentally revealed in cold atomic gases and it is expected to be a generic characteristic of any quench in a clean system with short range interactions. I will show, however, that the phenomenon of dynamical confinement of the elementary excitations has dramatic consequences for the non-equilibrium dynamics, in particular, the light cone structure gets significantly suppressed. Apart from being smoking gun signals of confinement, these effects allow for a quantitative study of the spectrum of the system, realizing a kind of "quench spectroscopy".