The present status of calculations of the hyperfine splitting and the trans
ition probability between the hyperfine splitting components in hydrogen- a
nd lithium-like ions is discussed. The results of the calculations are comp
ared with recent experimental data. A special attention is focused on the h
yperfine splitting in hydrogen-like lead and lithium-like bismuth. It is sh
own that the theoretical prediction for the ground state hyperfine splittin
g in lead based on the single particle nuclear model for the Bohr-Weisskopf
effect is in fair agreement with experiment. The theoretical prediction fo
r the ground state hyperfine splitting in lithium-like bismuth is improved
due to more accurate calculations of the interelectronic interaction, QED,
and nuclear corrections.