We present a new method, TrackSig, to estimate the evolutionary trajectories of signatures of somatic mutational processes. TrackSig infers an approximate order in which the somatic mutations accumulated, and then fits the signature exposures as a function of the ordering. Using simulations, we assess TrackSig's reconstruction accuracy. We find 1.9% median exposure error on simulations with one to three changepoints. The size and the direction of the signature change is consistent in 87% and 95% of cases respectively. There were an average of 0.02 missed change-points and 0.37 false positive change-points per sample. The code is available at https://github.com/YuliaRubanova/TrackSig.