Owing to the development of efficient algorithms and the improvement o
f computer power it is now possible to map out potential energy surfac
es (PESs) of reactions at surfaces in great detail. This achievement h
as been accompanied by an increased effort in the dynamical simulation
of processes on surfaces. The paradigm for simple reactions at surfac
es - the dissociation of hydrogen on metal surfaces - can now be treat
ed fully quantum dynamically in the molecular degrees of freedom from
first principles, i.e., without invoking any adjustable parameters. Th
is 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 surfac
es will be discussed. In addition, the ab initio molecular dynamics tr
eatment of reactions of hydrogen atoms with hydrogen-passivated semico
nductor surfaces and recent achievements in the ab initio description
of laser-induced desorption and further developments will be addressed
.