We argue that looking at steady states in dynamical models often lacks relevance for economists when convergence time is excessively long, especially since steady-state outcomes and pre-convergence behavior can radically differ. In such cases, understanding the behavior preceding convergence becomes of greater importance. Quasi-Stationary Distributions describe the behavior of stochastic processes before they converge to their steady states. We develop deterministic approximation techniques to qualitatively describe these objects, as population size gets large, for a large class of Markovian models.