We present a critical review of the state of the art of magnetic particle hyperthermia (MPH) as a minimal invasive tumour therapy. Magnetic principles of heating mechanisms are discussed with respect to the optimum choice of nanoparticle properties. In particular, the relation between superparamagnetic and ferrimagnetic single domain nanoparticles is clarified in order to choose the appropriate particle size distribution and the role of particle mobility for the relaxation path is discussed. Knowledge of the effect of particle properties for achieving high specific heating power provides necessary guidelines for development of nanoparticles tailored for tumour therapy. Nanoscale heat transfer processes are discussed with respect to the achievable temperature increase in cancer cells. The need to realize a well-controlled temperature distribution in tumour tissue represents the most serious problem of MPH, at present. Visionary concepts of particle administration, in particular by means of antibody targeting, are far from clinical practice, yet. On the basis of current knowledge of treating cancer by thermal damaging, this article elucidates possibilities, prospects, and challenges for establishment of MPH as a standard medical procedure.