With the advent of sophisticated experimental techniques to study various dynamical processes on solid surfaces, e.g., initial molecular state preparation, energy- and state-resolved detection techniques, the study of dynamical processes occurring on solid surfaces is now at the stage where there is a more direct link between what experimental studies observe and what theory predicts. It would not be an exaggeration to say that, in surfaces we have a playground for physics, and the study of dynamical processes occurring on solid surfaces, such as the ones mentioned above, is a rich field for new discoveries and observations of novel physical phenomena, filled with many possibilities. The most natural test particle of choice for these reactions is hydrogen, which has always played a central role in the development of modern physics. Of the several dynamical factors that influence the dynamics of hydrogen-solid surface reactions (e.g., relative coordinates of reactions partners-hydrogen molecule and solid surface, molecular internal degrees of freedom, surface degrees of freedom), one important factor is molecular orientation. In this review, we will consider the dissociative adsorption and associative desorption dynamics of H-2(D-2) molecules on/from Cu and Pd surfaces, which are typical examples of an activated and a non-activated system, respectively, and discuss how the orientation affects the dynamics of hydrogen on these surfaces and brings about such dynamical processes as steering and dynamical quantum filtering. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.