We analyze labor market models where the law of one price does not hold; i.e., models with equilibrium wage dispersion. We begin assuming workers are ex ante heterogeneous, and highlight a flaw with this approach: if search is costly, the market shuts down. We then assume workers are homogeneous but matches are ex post heterogeneous. This model is robust to search costs, and delivers equilibria equilibrium wage dispersion. However, we prove the law of two prices holds: generically we cannot get more than two wages. We explore several other models, including one combining ex ante and ex post heterogeneity; this model is robust, and can deliver more than two-point wage distributions.