The ignition process of condensed-phase combustion by a laser is studied experimentally as well as numerically. Numerical simulations are performed in one, two and three spatial dimensions, and are compared with the experimental observations. The effects of energy-dissipative mechanisms, such as melting and ablation due to laser irradiation and the effects of laser power output fluctuations, are also studied. We find that the ignition process depends mainly on the energy deposited in the system. The time leading up to ignition is longer for higher light fluxes keeping the average laser power constant, since a larger fraction of the energy is reradiated from the heated surface or consumed during the process of material removal.