The radiation produced by an arbitrarily moving relativistic charge in an absorbing medium is considered in terms of the radiation energy loss. The energy-angular distributions of emitted photons for Cherenkov radiation, prompt bremsstrahlung, and uniform motion over finite distance (the Tamm problem) are derived. The Doppler effect in an absorbing medium for undulator-like motion is considered. The high-energy, low-angle approximation of the spectra is discussed in terms of the complex formation zone of the radiation produced by an ultra-relativistic charge in an absorbing medium.