The present status of calculations of the hyperfine splitting and the transition probability between the hyperfine splitting components in hydrogen- and lithium-like ions is discussed. The results of the calculations are compared with recent experimental data. A special attention is focused on the hyperfine splitting in hydrogen-like lead and lithium-like bismuth. It is shown that the theoretical prediction for the ground state hyperfine splitting in lead based on the single particle nuclear model for the Bohr-Weisskopf effect is in fair agreement with experiment. The theoretical prediction for the ground state hyperfine splitting in lithium-like bismuth is improved due to more accurate calculations of the interelectronic interaction, QED, and nuclear corrections.