Several Equilibrium and non-equilibrium aspects of the classical  phi4 theory in 1+1 spatial dimensions are presented. At equilibrium the equivalence between the classical partition function and the quantum transfer matrix for the anharmonic oscillator allows to obtain exact results which provide a set of criteria for thermalization.   The non-equilibrium dynamics obtained by evolving the equations of motion in light-cone coordinates with large energy density show several distinct stages, all characterized by a cascade of energy towards the ultraviolet. After an initial transient stage, the spatio-temporal gradient terms become larger than the non-linear term, and there emerges a stage of "universal cascade", independent of the UV cutoff as well as of the initial conditions, with an effective infrared thermalization  at a slowly varying temperature determined solely by the energy density.