The Virtual Element Method (in short VEM, born in 2013) is a recent generalization of the Finite Element Method. By avoiding the explicit integration of the shape functions that span the discrete Galerkin space and introducing a novel construction of the associated stiffness matrix, the VEM acquires very interesting properties with respect to more standard Galerkin methods. For instance, the VEM easily allows for polygonal/polyhedral meshes including non-convex elements and still yields a conforming solution with (possibly) high order accuracy. In the present talk we introduce a discrete Stokes complex (in two space dimensions) made of Virtual Element spaces [3], thus suitable for general polygonal meshes and general order of accuracy. The pro- posed discrete Hilbert complex can be used to approximate problems in incompressible fluid dynamics, as it will be shown in the companion talk by Giuseppe Vacca [1, 2]. After presenting the discrete velocity and the discrete pressure space, we will describe the space of discrete scalar stream function. We will show how the associated Degrees of Freedom are built in order to guarantee both (1) the computability of the associated differential operators and (2) the computability of suitable projection operators needed for the approximation. A hint on the three dimensional case will also be given [4]. [1] L.BeiraodaVeiga, C.Lovadina, G.Vacca. Divergence free virtual elements or the Stokes problem on polygonal meshes. Math. Mod. Numer. Anal. Vol. 51, pp. 509–535, 2017. [2] L. Beirao da Veiga, C. Lovadina, G. Vacca. Virtual elements for the Navier-Stokes problem on polygonal meshes. SIAM J. Numer. Anal., Vol. 56, pp. 1210–1242, 2018. [3] L. Beirao da Veiga, D. Mora, G. Vacca. The Stokes complex for virtual elements with application to Navier-Stokes flows. J. Sci. Comp., Vol. 81, pp. 990–1018, 2019. [4] L. Beirao da Veiga, F. Dassi, G. Vacca. The Stokes complex for Virtual Elements in three dimen- sions. Math. Mod. and Meth. Appl. Sci., Vol. 30, pp. 477–512, 2020.