Fellegi and Sunter (1969) introduced the first theory of record linkage. Their work was interpreted and applied in many situations. But an infrastructure to support generalizing the F-S theory is not available until 40 years later. Sadinle and Fienberg (2013) discuss partitioning as a possible infrastructure for record linkage. Partitioning makes clear the limitations of F-S and paves the way to generalizing it. Partitioning also fits naturally in the Bayesian paradigm. We review the advent and instances of partitioning in the recent literature in particular in the context of linking applications connected to Dirichlet-Multinomial processes. We suggest directions for the future.