  Theoretical calculations of the Lamb shift provide the basis required for the
determination of the Rydberg constant from spectroscopic measurements in
hydrogen. The recent high-precision determination of the proton charge radius
drastically reduced the uncertainty in the hydrogen Lamb shift originating from
the proton size. As a result, the dominant theoretical uncertainty now comes
from the two- and three-loop QED effects, which calls for further advances in
their calculations. We review the present status of theoretical calculations of
the Lamb shift in hydrogen and light hydrogen-like ions with the nuclear charge
number up to $Z = 5$. Theoretical errors due to various effects are critically
examined and estimated.
