As a form of matter intermediate between molecules and bulk solids, atomic clusters have been much studied .Light-induced processes in clusters can lead to photo-fragmentation [2,3] and Coulombic fission , producing atom and ion fragments with a few electronvolts (eV) of energy. However, recent studies of the photoionization of atomic clusters with high intensity (>1016 W cm-2) femtosecond laser pulses have shown that these interactions can be far more energetic [5-13] -excitation of large atomic clusters can produce a superheated microplasma that ejects ions with kinetic energies up to 1 MeV . This phenomenon suggests that through irradiation of deuterium clusters, it would be possible to create plasmas with sufficient average ion energy for substantial nuclear fusion. Here we report the observation of nuclear fusion from the explosions of deuterium clusters heated with a compact, high-repetition-rate table-top laser. We achieve an efficiency of about 105 fusion neutrons per joule of incident laser energy, which approaches the efficiency of large-scale laser-driven fusion experiments. Our results should facilitate a range of fusion experiments using small-scale lasers, and may ultimately lead to the development of a table-top neutron source, which could potentially find wide application in materials studies.