In a gravitational context, canonical methods offer an intuitive picture of the dynamics and simplify a characterization of the degrees of freedom. In this talk, the canonical formulation of general variational discrete systems featuring evolving phase spaces will be presented. Attention will be devoted to a characterization of the arising constraints and degrees of freedom which differs somewhat from the continuum analogue. A particular application of these new tools pertains to discrete gravity models and allows for a novel perspective on their dynamics. This new formalism can also be viewed as an algorithm to generate solutions and may thereby be interesting for numerical implementations.