Studies of the quantum dynamics of isolated systems are currently providing fundamental insights into how statistical mechanics emerges under unitary time evolution. Thermalization seems ubiquitous, but experiments with ultracold gases have shown that it need not always occur, particularly near an integrable point. Unfortunately, computational studies of generic (nonintegrable) models are limited to small systems, for which arbitrarily long times can be calculated, or short times, for which large or infinite system sizes can be solved. Consequently, what happens in the thermodynamic limit after long times has been inaccessible to theoretical studies. In this talk, we introduce a linked-cluster based computational approach that allows one to address the latter question in lattice systems. We provide numerical evidence that, in the thermodynamic limit, thermalization occurs in the nonintegrable regime but fails at integrability. A phase transition-like behavior separates the two regimes.