The basic properties and concepts of dynamic systems theory are introduced by means of an imaginary, literary example, namely, Alice (from Wonderland) walking to the Queen in Through the Looking Glass (Carroll, 1871). The discussion encompasses notions such as time evolution, evolution term, attractor, self-organization, and timescales. These abstract notions are then applied to the study of first language (L1) and second language (L2) acquisition. The steps that should be taken toward the construction of dynamic systems models of L2 learning are described, including a discussion of the difficulties and the theoretical opportunities that accompany this model building. Finally, a concrete example of model building and of the study of variability as an indicator of developmental transitions in L1 acquisition is given.