  In the present paper we initiate the study of $hp$ Virtual Elements. We focus
on the case with uniform polynomial degree across the mesh and derive
theoretical convergence estimates that are explicit both in the mesh size $h$
and in the polynomial degree $p$ in the case of finite Sobolev regularity.
Exponential convergence is proved in the case of analytic solutions. The
theoretical convergence results are validated in numerical experiments.
Finally, an initial study on the possible choice of local basis functions is
included.
