  An explicit and computable error estimator for the $hp$ version of the
virtual element method (VEM), together with lower and upper bounds with respect
to the exact energy error, is presented. Such error estimator is employed to
provide $hp$ adaptive mesh refinements for very general polygonal meshes. In
addition, a novel VEM $hp$ Cl\'ement quasi-interpolant, instrumental for the a
posteriori error analysis, is introduced. The performances of the adaptive
method are validated by a number of numerical experiments.
