The current status of fundamental physics that govern nanoparticle magnetism is reviewed. Emphasis is placed on studies of the particles' intrinsic spin structure as influenced by surface and finite-size effects. Theories of dynamic spin fluctuation and spin reversal processes for uniaxial, isolated magnetic nanoparticles are presented, as applied primarily to the interpretation of magnetization and Mossbauer spectroscopic measurements. Monte Carlo simulation studies that corroborate experimental findings and advance elucidation of core vs. surface contributions to magnetic behavior are also presented. In addition, applications to nano and bio technology and future research directions in core/shell, matrix embedded and interacting magnetic nanoparticles are also addressed. (C) 2009 Published by Elsevier Ltd.