We develop a random search model with two-sided heterogeneity and match-specific productivity shocks to explain why high-productivity workers tend to work at high-productivity firms despite low-productivity workers gaining about as much from such matches. Our model has two key predictions: i) the average log wage that a worker receives is increasing in the worker's and employer's productivity, with low-productivity workers gaining proportionally more at high-productivity firms and ii) there is assortative matching between a worker's productivity and that of her employer. Selective job acceptance drives these patterns. All workers are equally likely to meet all firms, but workers have higher surplus from meeting firms of similar productivity. The high surplus meetings result in matches more frequently, generating assortative matching. Only the subset of meetings that result in matches are observed in administrative wage data, shaping wages. We show that our findings are quantitatively consistent with recent empirical results. Moreover, we prove this selection is not detected using standard empirical approaches, highlighting the importance of theory-guided empirical work. Our results imply that encouraging high-wage firms to hire low-wage workers may be less effective at reducing wage inequality than wage patterns suggest.