  We derive an anisotropic a posteriori error estimate for the adaptive
conforming Virtual Element approximation of a paradigmatic two-dimensional
elliptic problem. In particular, we introduce a quasi-interpolant operator and
exploit its approximation results to prove the reliability of the error
indicator. We design and implement the corresponding adaptive polygonal
anisotropic algorithm. Several numerical tests assess the superiority of the
proposed algorithm in comparison with standard polygonal isotropic mesh
refinement schemes.
