A review is given of the current status of theoretical and experimental investigations of laser thermonuclear fusion. A wide range of physical problems encountered in fusion research and ways of solving them are discussed. Attention is concentrated on current problems such as fusion energetics, adiabatic target compression, conditions for development of hydrodynamic instabilities, absorption of laser radiation in plasma, and plasma heating. Detailed analysis is made of the results of numerical fusion simulations that have been carried out subject to various assumptions relating to the type of target, laser pulse parameters, and predominant processes in the laser plasma. Some results are given of recent.