This lecture presents the gyrokinetic framework and details the various numerical schemes used in nonlinear simulations to compute turbulent transport in magnetic fusion plasmas. The basic features of tokamak magnetic configuration and of fusion plasmas are recalled. Fundamental elements of the gyrokinetic theory are carefully introduced, including the derivation of velocity drifts and of the quasi-neutrality. From the numerical point of view, the main focus is put on the three existing classes of numerical methods, namely Particle-In-Cell, Eulerian and semi-Lagrangian. Their properties are discussed, and their strengths and weaknesses are exhaustively reviewed.