  We present in a unified framework new conforming and nonconforming Virtual
Element Methods (VEM) for general second order elliptic problems in two and
three dimensions. The differential operator is split into its symmetric and
non-symmetric parts and conditions for stability and accuracy on their discrete
counterparts are established. These conditions are shown to lead to optimal
$H^1$- and $L^2$-error estimates, confirmed by numerical experiments on a set
of polygonal meshes. The accuracy of the numerical approximation provided by
the two methods is shown to be comparable.
