  We review aspects of loop quantum gravity in a pedagogical manner, with the
aim of enabling a precise but critical assessment of its achievements so far.
We emphasise that the off-shell (`strong') closure of the constraint algebra is
a crucial test of quantum space-time covariance, and thereby of the
consistency, of the theory. Special attention is paid to the appearance of a
large number of ambiguities, in particular in the formulation of the
Hamiltonian constraint. Developing suitable approximation methods to establish
a connection with classical gravity on the one hand, and with the physics of
elementary particles on the other, remains a major challenge.
