Nanocomposites have been shown to significantly reduce the peak heat release rate, as measured by cone calorimetry, for many polymers but they typically have no effect on the oxygen index or the UL-94 classification. In this review, we will cover what is known about the processes by which nanocomposite formation may bring this about. Montmorillonite will be the focus in this paper but attention will also be devoted to other materials, including carbon nanotubes and layered double hydroxides. A second section will be devoted to combinations of nanocomposite formation with conventional (and unconventional) fire retardants. The paper will conclude with a section attempting to forecast the future.