We consider collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature. Such sequences may arise from dilating about infinite time singularities. For finite time singularities no collapse can occur by a result Perelman. Using Fukaya theory, we study some geometric (not topological) aspects of such collapse. When the limit solution is 1-dimensional we construct a virtual 2-dimensional rotationally symmetric limit. This is joint work with David Glickenstein and Peng Lu.