This chapter takes a critical look at complexity in L2 research. We demonstrate several problems in the L2 literature in terms of how complexity has been defined and operationalised as a construct. In the first part of the chapter we try to unravel its highly complex, multidimensional nature by presenting a taxonomic model that identifies major types, dimensions and components of L2 complexity, each of which can be independently analysed or measured. The second part evaluates how complexity has been measured in empirical SLA research. Using the taxonomy of L2 complexity from part 1 as a framework, we inventory the measures of L2 complexity that have been used in a sample of forty recent L2 studies. Next we discuss the construct validity of several widely used measures of grammatical complexity by identifying their underlying logic as well as the methodological and practical challenges that their computation presents. (Contains 3 figures, 3 tables, and 7 footnotes.) [For complete volume, see ED539539.]