Research on second language (L2) acquisition in the generative tradition (GenSLA) addresses the nature of interlanguage competence, examining the roles of Universal Grammar, the mother tongue and the input in shaping the acquisition, representation and use of second languages. This field is sometimes dismissed by applied linguists as irrelevant because it does not provide direct applications for language teaching. However, the assumption that theories "must" have applications involves a fundamental misconception: linguistic theories explore the nature of grammar; GenSLA theories explore the nature of language learning. No such theory entails that language must be taught in a particular way. Nevertheless, potential applications can be identified: examples are presented that describe aspects of language that do not need to be taught, properties that might benefit from instruction, and cases where textbooks provide inadequate information. I argue that linguistic theory and GenSLA theory have more to offer in terms of considering what aspects of language might or might not be taught rather than how languages should be taught.