Research into the interaction between powerful laser radiation and plasma is reviewed in the context of laser fusion. Topics discussed include absorption and scattering of laser radiation by plasmas and the transfer of heat from the region in which absorption takes place to denser plasma layers. It is shown that parametric processes that lead to anomalous (nonclassical) absorption and scattering of laser radiation by plasmas do not prevent the attainment of laser energies of the order of kilojoules or dozens of kilojoules. The main problems that await investigation before existing data can be extended to the megajoule range that is necessary for the ignition effusion reactions by lasers are reviewed.