Quantum electrodynamic perturbation theory is applied to high-Z few-electron atoms. The starting point is the Dirac equation for an electron in the external field of the nucleus. Interaction of the bound electrons with the quantized electromagnetic field is treated as a perturbation that results in the electron-electron interaction and radiative corrections. The energy-level shifts caused by this interaction are examined for one-, two-, and three-electron ions in the first and second orders in a and in the first order in m/M. Calculations of the QED and nuclear corrections to the hyperfine splitting in hydrogenlike and lithiumlike ions are considered as well. The currently available theoretical results for the Lamb shift, the hyperfine splitting, and the bound-electron g-factor are compared with recent experiments.