In this paper, we summarize our recent work on gyrokinetic applications in electron- positron and non-neutral plasma. The electrostatic stability of electron-positron plasmas was investigated in dipole and slab geometry, with and without ion admixture. The gyrokinetic dispersion relation was derived and, for the slab case, extended to non-neutral plasmas. Here, we further extend the gyrokinetic formulation to the relativistic regime.