A search for the direct production of charginos and neutralinos in final states with three leptons and missing transverse momentum is presented. The analysis is based on 20.3 fb-1 of vs = 8TeV proton-proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with the Standard Model expectations and limits are set in R-parity-conserving phenomenological Minimal Supersymmetric Standard Models and in simplified supersymmetric models, significantly extending previous results. For simplified supersymmetric models of direct chargino (∼X±1) and next-to-lightest neutralino (X∼02) production with decays to lightest neutralino (∼X01) via either all three generations of sleptons, staus only, gauge bosons, or Higgs bosons, ∼X± 1 and ∼X02 masses are excluded up to 700GeV, 380GeV, 345GeV, or 148GeV respectively, for a massless ∼X01.