  We define a generalization of virtual links to arbitrary dimensions by
extending the geometric definition due to Carter et al. We show that many
homotopy type invariants for classical links extend to invariants of virtual
links. We also define generalizations of virtual link diagrams and Gauss codes
to represent virtual links, and use such diagrams to construct a combinatorial
biquandle invariant for virtual $2$-links. In the case of $2$-links, we also
explore generalizations of Fox-Milnor movies to the virtual case. In addition,
we discuss definitions extending the notion of welded links to higher
dimensions. For ribbon knots in dimension $4$ or greater, we show that the knot
quandle is a complete classifying invariant up to taking connected sums with a
trivially knotted $S^1\times S^{n-1}$, and that all the isotopies involved may
be taken to be generated by stable equivalences of ribbon knots.
