Conventional crystallography was developed under the explicit assumption that crystalline objects exhibit ideal periodicity in three dimensions. However, in the last half-century, new aperiodic structures have been discovered or rediscovered that lack translational symmetry in three dimensions but can be described using higher-dimensional approaches, for example, modulated structures and quasicrystals. Additionally, advances in neutron crystallography of magnetic materials have necessitated a comprehensive description of magnetic symmetry. These non-traditional forms of crystallographic symmetry are discussed here both for completeness and to provide the reader with an overview of recent developments in this long-established field.