The phenomenon of quantum tunneling of magnetization (QTM) may be destined to play a significant role within the next two decades in limiting the density of information storage in magnetic systems. Recent advances, indeed, indicate that this limit may well be reached even earlier. One of the most controversial issues in the field is how to establish reliable criteria to determine whether experimental results do indeed reveal manifestations of QTM. Much progress on this issue is reported here. <br/> <em>Audience</em>: While some articles are tutorial in nature, the book is primarily directed to those already working on QTM, no matter what their background.