[en] The NMR chemical shift spectra of diamond, chemical-vapor-deposited (CVD) diamond, and diamondlike amorphous carbon are computed from first principles. The results of our calculation are in excellent agreement with experiments, and are useful for the interpretation of the NMR spectra in terms of the microscopic structure of the materials. In particular, we show that the NMR and Raman linewidths in polycrystalline CVD diamond are due to stress fluctuations, and we support a heterogeneous model for the amorphous hydrogenated phase. copyright 1997 The American Physical Society