The distribution of wages and jobs changed all across advanced economies the last few decades. These changes came seemingly unexpected. Economic theory tell us to look at supply and demand to understand what happened. In practice, we cannot directly observe demand and supply shifts. We also cannot easily distinguish the economic forces behind these distributional changes from other concurrent phenomena. These fundamental problems permeate all studies of changes in the wage and occupational distributions. This dissertation applies two approaches to overcome these challenges. In the first chapter (with Tzuo-Hann Law), we take an assortative matching model with on-the-job search and use it understand what forces drove up wage inequality in Germany between the 1990s and 2000s. The model conceives of a worker's ability and a firm's productivity as one-dimensional, rankable indices, which we non-parametrically identify. With these productivity ranks, we identify production technology. The model fits wages almost as well as statistical decompositions that use more degrees of freedom. This model fit gives us confidence to make inference with the model. We find that changes in production technology and the equilibrium sorting patterns it induces account for the rise in wage dispersion. Search frictions had little impact on its rise over time. The approach in the first chapter works well to account for rising wage inequality. However, it misses out on another important change - the decline in traditionally middle-wage jobs or job polarization. In the second chapter, I present a multidimensional skills search model which accounts for changes in occupational wages, occupational employment shares, and the wage distribution at large. In contrast to the first chapter, this model takes a parametric approach but still reproduces numerous aspects of US cross sectional data observed from 1979 to 2010. The model indicates industry trends and technological progress account for the majority of these changes. Information and communications technology spurred demand for jobs requiring interpersonal and social skills in the 1990s. This development appears farther reaching than the automation of jobs concentrated in the manufacturing and construction sectors.