I study the matching of heterogeneous workers and firms in the labor market. In particular, I examine how firm productivity shocks and the nature of decreasing returns affect positive assortative matching: outcomes where the best, most productive workers are employed by the most productive firms and the least productive workers are assigned to the least productive firms. Chapter one studies the relationship between worker-firm sorting and firm growth both empirically and theoretically. I use U.S. Census microdata to show that faster growing firms hire more productive workers, as measured by their lagged wages. This appears to be the first time that such a pattern has been documented. I interpret the pattern as evidence of positive assortative matching: faster growing, more productive firms tend to hire more productive workers. I develop a novel, analytically tractable search model and show that it can reproduce the observed patterns if there are strong complementarities in the production function. I also discuss the relationship between my empirical results and the previous literature on assortative matching. I argue that it is important to control for observable firm characteristics, which may proxy for the nature of the labor market facing the firm. Chapter two assesses the theoretical properties of several models, some novel and some drawn from the previous literature. I focus on each model's sufficient conditions for positive assortative matching. The models in the existing literature have a variety of sufficient conditions for positive sorting, and it has not been clear why these conditions vary across models. To answer this question I develop generalizations of each model that preserve their sorting properties. By comparing the generalized models I am able to show that the differences stem from how firm size, or scale, is dealt with. This result suggests caution when developing and interpreting models of sorting, since seemingly innocuous assumptions can result in significantly different behavior.