Virtual Knot theory is to classical knot theory as graphs are to planar graphs. In virtual knot theory we study Gauss codes representing "knots" that have an abstract existence, but require virtual crossings when one tries to draw them in the plane. In this generalization of classical knot theory, many new phenomena appear: There are non-trivial knots with trivial Jones polynomial.There are non-trivial knots with non-trivial Jones polynonmial, but with the infinite cyclic fundamental group. Quantum link invariants and Vassiliev invariants generalize to virtuals as does the fundamental group, rack and quandle. A conbinatorial theory of flat virtuals is interesting in its own right. Virtual braids can be analyzed and, surprisingly, virtuals have applications not only to knots and links in thickened surfaces but also to embeddingd of surfaces in four dimensional space.