In this article I discuss some key points that are raised in the papers in this special issue. The first issue is that a variety of theoretical tools are necessary for a complete understanding of the issues raised in these papers. Second, although the methodology that is used in studies of second language knowledge has improved, it is clear we still lack an agreed-on set of protocols that will permit reliable comparisons across studies. In spite of these challenges, we are making progress in using complementary theories of the role of lexical representation, predication, and crosslinguistic variation to get a full picture of this complex area of lexico-morphosyntactic knowledge.