  We present the essential instruments to deal with Virtual Element Method
(VEM) for the resolution of partial differential equations in mixed form.
Functional spaces, degrees of freedom, projectors and differential operators
are described emphasizing how to build them in a virtual element framework and
for a general approximation order. To achieve this goal, it was necessary to
make a deep analysis on polynomial spaces and decompositions. Finally, we
exploit such `briks' to construct virtual element approximations of Stokes,
Darcy and Navier-Stokes problems and we provide a series of examples to
numerically verify the theoretical behavior of high-order VEM.
