Children, at least children acquiring their native language (L1), develop grammars vastly underdetermined by the primary linguistic data available to them, converging on both obvious and subtle properties of the target language (TL), rapidly, (essentially) uniformly, and reflexively (i.e., without effort or intentional instruction). In contrast, (adult) nonnative language (L2) acquisition, even under optimal conditions of TL exposure, displays more varied outcomes, frequently with readily observable divergence from the TL, often despite concerted effort and instruction. The standard assumption in mainstream generative grammar is that (L1) children display target convergence because early language acquisition is guided and constrained by the set of innate domain-specific cognitive structures generally referred to as Universal Grammar (UG). This chapter considers conceptual issues surrounding as well as empirical evidence for and against the claim that (despite initial appearances) some or all of the principles and primes of UG likewise guide and constrain (adult) L2 acquisition.