Unlike most cosmic plasma structures, planetary magnetospheres can be extensively studied in situ. In particular, studies of the Earth's magnetosphere over the past few decades have resulted in a relatively good experimental understanding of both its basic structural properties and its response to changes in the impinging solar wind. In this article we provide a broad overview, designed for researchers unfamiliar with magnetospheric physics, of the main processes and parameters that control the structure and dynamics of planetary magnetospheres, especially the Earth's. In particular, we concentrate on the structure and dynamics of three important regions: the bow shock, the magnetopause and the magnetotail. In the final part of this review we describe the current status of global magnetospheric modelling, which is crucial to placing in situ observations in the proper context and providing a better understanding of magnetospheric structure and dynamics under all possible input conditions. Although the parameter regime experienced in the solar system is limited, the plasma physics that is learned by studying planetary magnetospheres can, in principle, be translated to more general studies of cosmic plasma structures. Conversely, studies of cosmic plasma under a wide range of conditions should be used to understand Earth's