These efforts were rewarded in 1994-96 by the first observations, in Europe and later the USA, of incoherent tunneling relaxation in the Mn-12 molecular magnet system. In the period 1999-2003 very extensive work was done on systems like Fe-8, V-15, and other molecular species, and the role of nuclear spins, phonons, intermolecular dipolar interactions, and the Berry spin topological phase, in the quantum relaxation of the molecular spins, was elucidated experimentally. In parallel developments, experiments in the USA on quantum spin glasses also found evidence for interesting quantum relaxation phenomena, later followed up in Europe.

There are however still a number of crucial challenges facing this now very large field. There is no convincing demontration of coherence or quantum control in these systems- a pre-requisite for their use in any quantum information processing system- even though some experiments give tantalising hints that this coherence must be there. To achive this goal, a number of crucial challenges must be met, both in the sysnthesis of new materials and their theoretical understanding, and new experimental techniques; and some of the decoherence processes in these systems remain mysterious. This PITP mini-workshop is inteneded to address these problems and suggest new strategies for their resolution.