A frequently heard query concerns why students receive relatively high grades in their mathematical school work and yet fail to be able to apply their mathematical knowledge and skills in contextual settings that they encounter in their other studies and their daily lives, not to mention meeting the mathematical challenges presented in subsequent mathematical courses. Many reform documents call for students to have opportunities to apply their mathematical knowledge in modeling settings and to reason and make sense of quantitative, spatial, or data-intensive situations (NCTM, 2000, 2009). The acquisition of such modeling expertise was a central focus of the 2004 ICMI conference at the University of Dortmund and this ICMI volume that documents the plenary presentations and issue papers related to themes discussed at or emerging from that meeting. What are the barriers that stand in the way of developing the adaptive expertise called for by modeling challenges?