I will present my recent work on generalized mimetic theories of gravity. I will show that general scalar-tensor theories are invariant under disformal transformations. However for non-invertible transformations one obtains new theories that are generalizations of the mimetic dark matter scenario. Simple mimetic models can have the same expansion history as LCDM. I will discuss linear scalar perturbations in mimetic Horndeski gravity and show: i) the sound speed is exactly zero, ii) the comoving curvature perturbation is constant on all scales. Furthermore, the system does not have any wave-like scalar degrees of freedom (dof) around any background. Time permitting, I will present a way to introduce propagating dof but show that it suffers from either gradient or ghost instabilities. In the ghost branch of the model, the time scale of the instability is estimated and shown to be phenomenologically viable and thus the mimetic dark matter scenario is a viable alternative to the dark matter paradigm.