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A pseudodiagram is a diagram of a knot with some crossing informationmissing. We review and expand the theory of pseudodiagrams introduced by R.Hanaki. We then extend this theory to the realm of virtual knots, ageneralization of knots. In particular, we investigate how much crossinginformation must be known to conclude that a diagram is a diagram of the unknot(the trivializing number). We also consider how much information is necessaryto identify a non-trivial knot, a classical knot, or a non-classical knot. Wethen apply pseudodiagram theory to develop new upper bounds on unknottingnumber, virtual unknotting number, and genus.

Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus