About ten years ago it was shown theoretically that after a sudden ionization the electronic many-body effects alone can beget rich ultrafast electron dynamics. The positive charge created after the ionization can migrate throughout the system on a femtosecond time scale solely driven by the electron correlation and electron relaxation. Although typical for the inner-valence ionized states, it appeared only recently that this charge migration phenomenon can also take place after ionization out of the outer-valence shell. The ab initio method for multielectron wave-packet propagation developed for treating electron dynamics following ionization will be presented. The approach is equally suitable for tracing in real time and space the electron dynamics of both decaying and non-decaying electronic states. Results from calculations on different systems will be presented and the mechanisms underlying the charge migration will be analyzed in terms of simple models. The possibilities for experimental verification of the phenomenon will also be discussed. In particular, it will be shown that the charge migration may produce a measurable IR radiation.