The ALICE collaboration at the CERN LHC reports novel measurements of jet substructure in pp collisions at s=7 TeV and central Pb–Pb collisions at sNN=2.76 TeV. Jet substructure of track-based jets is explored via iterative declustering and grooming techniques. We present the measurement of the momentum sharing of two-prong substructure exposed via grooming, the zg, and its dependence on the opening angle, in both pp and Pb–Pb collisions. We also present the measurement of the distribution of the number of branches obtained in the iterative declustering of the jet, which is interpreted as the number of its hard splittings. In Pb–Pb collisions, we observe a suppression of symmetric splittings at large opening angles and an enhancement of splittings at small opening angles relative to pp collisions, with no significant modification of the number of splittings. The results are compared to predictions from various Monte Carlo event generators to test the role of important concepts in the evolution of the jet in the medium such as colour coherence.