  We introduce a notion of intrinsic linking and knotting for virtual spatial
graphs. Our theory gives two filtrations of the set of all graphs, allowing us
to measure, in a sense, how intrinsically linked or knotted a graph is; we show
that these filtrations are descending and non-terminating. We also provide
several examples of intrinsically virtually linked and knotted graphs. As a
byproduct, we introduce the {\it virtual unknotting number} of a knot, and show
that any knot with non-trivial Jones polynomial has virtual unknotting number
at least 2.
