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We review c-field methods for simulating the non-equilibrium dynamics ofdegenerate Bose gases beyond the mean-field Gross-Pitaevskii approximation. Wedescribe three separate approaches that utilise similar numerical methods, buthave distinct regimes of validity. Systems at finite temperature can be treatedwith either the closed-system projected Gross-Pitaevskii equation (PGPE), orthe open-system stochastic projected Gross-Pitaevskii equation (SPGPE). Theseare both applicable in quantum degenerate regimes in which thermal fluctuationsare significant. At low or zero temperature, the truncated Wigner projectedGross-Pitaevskii equation (TWPGPE) allows for the simulation of systems inwhich spontaneous collision processes seeded by quantum fluctuations areimportant. We describe the regimes of validity of each of these methods, anddiscuss their relationships to one another, and to other simulation techniquesfor the dynamics of Bose gases. The utility of the SPGPE formalism in modellingnon-equilibrium Bose gases is illustrated by its application to the dynamics ofspontaneous vortex formation in the growth of a Bose-Einstein condensate.

C-Field Methods for Non-Equilibrium Bose Gases