Conversion of intense laser radiation into incoherent thermal X rays and confinement of the X-ray radiation within a cavity are effective to overcome nonuniform energy deposition to a fusion pellet arising from the direct laser irradiation. We describe here the present understanding of the radiation confinement in cavities heated by lasers. Principles of the confinement are explained by the theoretical model treating a radiation heat wave propagating through the wall of a cavity. Experimental results on radiation confinement obtained under the joint program between ILE-Osaka and MPQ-Garching by using the Gekko XII glass laser system are briefly reported.