This talk is an introduction to virtual knot theory and a discussion of invariants of virtual knots and virtual knot cobordism. Virtual knot theory is a generalization of classsical knot theory that has a diagrammatic system similar to the classical Reidemeister moves and studies embeddings of knots in thickened surfaces. Many fascinating phenomenal appear in this theory and it sheds light on the problem of whether the Jones polynomial detects the unknot.