The magnetic properties of nanoparticles of antiferromagnetic materials are reviewed. The magnetic structure is often similar to the bulk structure, but there are several examples of size-dependent magnetic structures. Owing to the small magnetic moments of antiferromagnetic nanoparticles, the commonly used analysis of magnetization curves above the superparamagnetic blocking temperature may give erroneous results, because the distribution in magnetic moments and the magnetic anisotropy are not taken into account. We discuss how the magnetic dynamics can be studied by use of magnetization measurements, Mössbauer spectroscopy and neutron scattering. Below the blocking temperature, the magnetic dynamics in nanoparticles is dominated by thermal excitations of the uniform mode. In antiferromagnetic nanoparticles, the frequency of this mode is much higher than in ferromagnetic and ferrimagnetic nanoparticles, but it depends crucially on the size of the uncompensated moment. Excitation of the uniform mode results in a so-called thermoinduced moment, because the two sublattices are not strictly antiparallel when this mode is excited. The magnetic dipole interaction between antiferromagnetic nanoparticles is usually negligible, and therefore such particles present a unique possibility to study exchange interactions between magnetic particles. The interactions can have a significant influence on both the magnetic dynamics and the magnetic structure. Nanoparticles can be attached with a common crystallographic orientation such that both the crystallographic and the magnetic order continue across the interfaces.