  We review here the studies performed about interactions in an assembly of
cold Rydberg atoms. We focus more specially the review on the dipole-dipole
interactions and on the effect of the dipole blockade in the laser Rydberg
excitation, which offers attractive possibilities for quantum engineering. We
present first the various interactions between Rydberg atoms. The laser Rydberg
excitation of such an assembly is then described with the introduction of the
dipole blockade phenomenon. We report recent experiments performed in this
subject by starting with the case of a pair of atoms allowing the entanglement
of the wave-functions of the atoms and opening a fascinating way for the
realization of quantum bits and quantum gates. We consider then several works
on the blockade effect in a large assembly of atoms for three different
configurations: blockade through electric-field induced dipole, through
F\"orster resonance and in van der Waals interaction. The properties of
coherence and cooperativity are analyzed. Finally, we treat the role of
dipole-dipole interactions between Rydberg atoms responsible for Penning
ionization. The perturbation of the dipole blockade by ions and the evolution
of the Rydberg towards an ultracold plasma are discussed.
