Hamiltonian and action principle formulations of the basic equations of plasma physics are reviewed. Various types of Lagrangian and Poisson bracket formulations for kinetic and fluid theories are discussed, and it is described how such formulations can be used to derive and approximate physical models. Additional uses are also described. Two applications are treated in greater detail: an algorithm based on Dirac brackets for the calculation of V-states of contour dynamics and the calculation of fluctuation spectra of Vlasov theory and shear flow dynamics by methods of statistical mechanics.
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