Atomic binding energies are calculated at utmost precision. A report on the
current status of Lamb-shift predictions for hydrogenlike ions, including
all quantum electrodynamical corrections to first and second order in the f
ine structure constant alpha is presented. All relevant nuclear effects are
taken into account. High-precision calculations for the Lamb shift in hydr
ogen are presented. The hyperfine structure splitting and the g factor of a
bound electron in the strong electromagnetic field of a heavy nucleus is c
onsidered. Special emphasis is also put on parity violation effects in atom
ic systems. For all systems possible investigations beyond precision tests
of quantum electrodynamics are considered.