The discovery of molecular nanomagnets showing novel quantum effects, as the quantum tunneling of the magnetization, has brought to a renewed interest for the study of molecular magnetism and multifunctional molecular material. These materials have recently triggered an intense research activity in view of their possible applicabilities as, for example, as nanosized information storage units and as magnetic nanoparticles for bio-medicine. Several fundamental aspects of the microscopic static and dynamic properties of these molecular materials have been obtained by means of spectroscopies using local probes, as nuclei and muons. In this book an extensive overview on the results obtained during the last decade and on recent achievements in the study of molecular magnets by means of Nuclear Magnetic Resonance, Muon Spin Rotation, Magnetic Resonance Imaging and Mossbauer techniques is presented. The aim is to introduce the reader to these techniques and to give a general background on their application to molecular spin systems.