This review is devoted to the study of ultrafast laser ablation of solids and liquids. The ablation of condensed matter under exposure to subpicosecond laser pulses has a number of peculiar properties which distinguish this process from ablation induced by nanosecond and longer laser pulses. The process of ultrafast ablation includes light absorption by electrons in the skin layer, energy transfer from the skin layer to target interior by nonlinear electronic heat conduction, relaxation of the electron and ion temperatures, ultrafast melting, hydrodynamic expansion of heated matter accompanied by the formation of metastable states and subsequent formation of breaks in condensed matter. In case of ultrashort laser excitation, these processes are temporally separated and can thus be studied separately. As for energy absorption, we consider peculiarities of the case of metal irradiation in contrast to dielectrics and semiconductors. We discuss the energy dissipation processes of electronic thermal wave and lattice heating. Different types of phase transitions after ultrashort laser pulse irradiation as melting, vaporization or transitions to warm dense matter are discussed. Also nonthermal phase transitions, directly caused by the electronic excitation before considerable lattice heating, are considered. The final material removal occurs from the physical point of view as expansion of heated matter; here we discuss approaches of hydrodynamics, as well as molecular dynamic simulations directly following the atomic movements. Hybrid approaches tracing the dynamics of excited electrons, energy dissipation and structural dynamics in a combined simulation are reviewed as well.