How does retrieval take place in recognition memory? A number of computational models have been developed that posit that recognition operates by a process of global matching, wherein the cue is compared to each stored memory. These cue-to-memory similarities are then aggregated to produce an index of the global similarity between the cue and the contents of memory which can then be subjected to a decision process. In this chapter, we describe a.) the theoretical rationale and successes of such models, such as their accounts of similarity and list-length effects and generalization to multiple memory tasks, b.) challenges and hurdles they have experienced, including the null list-strength effect, the mirror effect, and the extralist feature effect, and c.) recent developments, such as extensions to predictions about response latency, sources of interference outside of the study list, and integration of more realistic representations.