Tsyganenko’s work has significantly shaped the way the space research community interpret the magnetospheric structure and topology, and through that also the dynamic magnetospheric processes. It is hard to overstate the physical significance of the Tsyganenko models, given that the nature of the magnetic field is the key to understanding the structure and dynamics of the Earth’s magnetosphere, such as the connectivity along field lines from one part of the system to another, as well as stresses and momentum transfer via the field. Better than any alternative model, they define conditions within the inner magnetosphere, a region where kinetic effects make the development of global first-principle models extremely difficult. Tsyganenko has also published a number of articles exploring mathematical tools, as well as physical aspects and consequences of magnetospheric models.