Spin-lattice relaxation mechanisms of nuclear spins in solids in the presence of low concentrations of paramagnetic centers are discussed. Apart from the electron spin-lattice relaxation mechanism, three-spin processes involving two electron spins and a nuclear spin may also play a role in the spin-lattice relaxation of the nuclear spins. Nuclear spins that are close to a paramagnetic impurity center experience large local fields and do not contribute to the NMR signal. Only a small percentage of nuclear spins surrounding an impurity center are polarized directly. The majority of the nuclear spins are polarized by spin diffusion, which is a slow process. A brief overview of a number of paramagnetic impurity centers, which are common in natural diamond, is given and experimental 13 C spin-lattice relaxation times for a suite of natural diamonds are compared with calculated values.