In this talk, we will first review the idea of mimetic gravity in which the conformal mode of gravity isolates by means of a scalar field. In cosmological setup, an energy density component naturally arises which behaves like dark matter. We will show that the setup is, however, unstable at the level of perturbations and we will introduce some possible healthy extensions of this scenario. In the second part, replacing the scalar field with a general p-form, we find a new mimetic theory and we particularly focus on the case of one-form gauge potential. This model is free of instabilities and provides an energy density which behaves like spatial curvature in the cosmological background. We will discuss some cosmological implications of this model.