We report jet substructure measurements in pp and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ALICE detector. Charged-particle jets were reconstructed at midrapidity with the ALICE tracking detectors using the anti-$k_{\mathrm{T}}$ algorithm with resolution parameters $R=0.2$ and $R=0.4$. In pp collisions, the groomed jet momentum fraction, $z_{\mathrm{g}}$, and the groomed jet radius, $\theta_{\mathrm{g}} \equiv R_{\mathrm{g}}/R$, are measured for the first time using the Dynamical Grooming method. Additionally, new systematic measurements of the infrared and collinear (IRC) safe ungroomed jet angularities are presented. In heavy-ion collisions, we measure $z_{\mathrm{g}}$ and $\theta_{\mathrm{g}}$ with the Soft Drop grooming algorithm. The large underlying event in heavy-ion collisions poses a challenge for the reconstruction of groomed jet observables, since fluctuations in the background can cause groomed splitting to be misidentified. By using strong grooming conditions to reduce this background, we report these observables fully corrected for detector effects and background fluctuations for the first time, and compare them to several theoretical models.