We present a mean field theory to describe cholesteric elastomers and gels under an external field, such as an electric or a magnetic field, along the helix axis of a cholesteric phase. We study the deformations and volume phase transitions of cholesteric gels as a function of the external field and temperature. Our theory predicts the phase transitions between isotropic (I), nematic (N), and heliconical cholesteric (ChH) phases and the deformations of the elastomers at these phase transition temperatures. We also find volume phase transitions at the I−ChH and the N−ChH phase transitions.