  Due to the development of efficient algorithms and the improvement of
computer power it is now possible to map out potential energy surfaces (PES) of
reactions at surfaces in great detail. This achievement has been accompanied by
an increased effort in the dynamical simulation of processes on surfaces. The
paradigm for simple reactions at surfaces -- the dissociation of hydrogen on
metal surfaces -- can now be treated fully quantum dynamically in the molecular
degrees of freedom from first principles, i.e., without invoking any adjustable
parameters. This relatively new field of ab initio dynamics simulations of
reactions at surfaces will be reviewed. Mainly the dissociation of hydrogen on
clean and adsorbate covered metal surfaces and on semiconductor surfaces will
be discussed. In addition, the ab initio molecular dynamics treatment of
reactions of hydrogen atoms with hydrogen-passivated semiconductor surfaces and
recent achievements in the ab initio description of laser-induced desorption
and further developments will be addressed.
