The target chamber of an inertial confinement fusion (ICF) power plant or high-yield test facility must be designed to absorb the target produced Xrays and ions and survive the resulting effects. The target chamber conditions must be restored in fractions of a second for high repetition rate power applications. Computer modeling of these phenomena is essential because equivalent conditions cannot be produced in laboratory experiments prior to the first ignition of high-yield ICF targets. Choices of models are dictated by specific reactor design strategies. The two major strategies, gas protection and sacrificial first surfaces, are used as a guide to our discussion. Physical models for ion, electron, and X-ray deposition are discussed, along with physical and numerical modeling of the resulting phase changes intarget chamber structures. The hydrodynamics and radiative transfer in the target chamber vapors and plasmas are central topics.