The most widely used learning paradigm in Grammatical Inference was introduced in 1967 and is known as identification in the limit. An important issue that has been raised with respect to the original definition is the absence of efficiency bounds. Nearly fifty years after its introduction, it remains an open problem how to best incorporate a notion of efficiency and tractability into this framework. This chapter surveys the different refinements that have been developed and studied, and the challenges they face. Main results for each formalization, along with comparisons, are provided.