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This article reviews the status of several solutions to all the constraintsof quantum gravity that have been proposed in terms of loops and extendedloops. We discuss pitfalls of several of the results and in particular discussthe issues of covariance and regularization of the constraints in terms ofextended loops. We also propose a formalism for ``thickened out loops'' whichdoes not face the covariance problems of extended loops and may allow toregularize expressions in a consistent manner.Comment: 16 Pages, Revtex/epsf, one figure included

Knot polynomial states of quantum gravity in terms of loops and extended loops: Some remarks