In this work the High Order Mimetic Discretization Framework will be presented together with a discussion of two fundamental aspects for the construction of structure-preserving discretizations: (i) the definition of the discrete degrees of freedom of physical field quantities, and (ii) the formulation of the physical field laws. For the first, the geometric degrees of freedom (associated to point, lines, surfaces and volumes) will be introduced. For the second, the Navier Stokes equations will be used as an example.