This article discusses the magnetic properties of nanoparticles. It first considers magnetic domains and the critical size for single-domain behavior of magnetic nanoparticles before providing an overview of magnetic anisotropy in nanoparticles. It then examines magnetic dynamics in nanoparticles, with particular emphasis on superparamagnetic relaxation and the use of Mössbauer spectroscopy, dc magnetization measurements, and ac susceptibility measurements for studies of superparamagnetic relaxation. It also describes magnetic dynamics below the blocking temperature, magnetic interactions between nanoparticles, and fluctuations of the magnetization directions. Finally, it analyzes the magnetic structure of nanoparticles, focusing on magnetic phase transitions and surface effects, non-collinear spin structures, and magnetic moments of antiferromagnetic nanoparticles.