Single cell experiments provide an unprecedented opportunity to reconstruct a sequence of changes in a biological process from individual “snapshots” of cells. However, nonlinear gene expression changes, genes unrelated to the process, and the possibility of branching trajectories make this a challenging problem. We develop SLICER (Selective Locally Linear Inference of Cellular Expression Relationships) to address these challenges. SLICER can infer highly nonlinear trajectories, select genes without prior knowledge of the process, and automatically determine the location and number of branches and loops. SLICER recovers the ordering of points along simulated trajectories more accurately than existing methods. We demonstrate the effectiveness of SLICER on previously published data from mouse lung cells and neural stem cells.