Single molecule magnets (SMM) are a new type of magnetic nanostructure that consist of a core of strongly exchange-coupled transition metal ions with a large collective magnetic moment per molecule, thus far up to 20 Bohr magnetons. Their molecular nature enables experimental studies of monodisperse ensembles of nanomagnets with well-defined size, shape, chemical composition, and magnetic anisotropy. These materials are of interest for studies of the interplay between classical and quantum effects in nanomagnets and, potentially, for quantum information storage. This talk will present results of our recent magnetic studies of the crossover between thermal activation (superparamagnetism) and quantum tunneling of the magnetization in the prototype SMM Mn12-acetate. Some open questions in magnetic quantum tunneling in SMMs will also be discussed.