  First-principles plane wave calculations predict that Li can be adsorbed on
graphene forming a uniform and stable coverage on both sides. A significant
part of the electronic charge of the Li-$2s$ orbital is donated to graphene and
is accommodated by its distorted $\pi^*$-bands. As a result, semimetallic
graphene and semiconducting graphene ribbons change into good metals. It is
even more remarkable that Li covered graphene can serve as a high-capacity
hydrogen storage medium with each adsorbed Li absorbing up to four H$_2$
molecules amounting to a gravimetric density of 12.8 wt%.
