In this paper, we investigate several properties of the solution maps of variational inequalities with polynomial data. First, we prove some facts on the R_0-property, the local boundedness, and the upper semicontinuity of the solution maps. Second, we establish results on the solution existence and stability under the copositivity condition. Third, when the constraint set is semi-algebraic, we discuss the genericity of the R_0-property and the finite-valuedness of the solution maps.