We present a new method, TrackSig, to estimate evolutionary trajectories in cancer. Our method represents cancer evolution in terms of mutational signatures -- multinomial distributions over mutation types. TrackSig infers an approximate order in which mutations accumulated in cancer genome, and then fits the signatures to the mutation time series. We assess TrackSig's reconstruction accuracy using simulations. We find 1.9% median discrepancy between estimated mixtures and ground truth. The size of the signature change is consistent in 87% cases and direction of change is consistent in 95% of cases. The code is available at https://github.com/YuliaRubanova/TrackSig.