This is a tutorial review on systems theory and its applications to space plasma physics and, more broadly, on geophysics. With its basis on the state representation of a plasma the theory is widely applicable, but it is of particular interest for dynamical, nonlinear, or out-of-equilibrium regimes that cannot be represented by traditional microscopic modeling. Two distinct, but closely related, branches of the theory are applied when the plasma dynamics is traced to first principles and when it needs to be derived from experimental data. A framework of modeling methods is presented in order of increasing complexity: enumeration of the effective degrees of freedom, measurement of the linear dynamics and stability, and generalization to their nonlinear counterparts. The relation between symmetries in the plasma system and modes in its structure and response is discussed. Signal processing methods are presented, illustrated by examples, and their relative merits and limitations are discussed. The dynamical framework provides a new approach alongside the traditional perturbative and statistical-mechanical methodologies and is directly relevant to the development of space weather applications.