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