Graded Clifford algebras are non-commutative graded algebras that are related to classical Clifford algebras, and one can read off certain properties of such an algebra from certain commutative geometric data associated to the algebra. In particular, a standard result is that a graded Clifford algebra C is quadratic and Artin-Schelter regular with Hilbert series equal to that of a polynomial ring if and only if a certain quadric system associated to C is base-point free. About ten years ago, T. Cassidy and the speaker introduced a generalization of such an algebra, called a graded skew Clifford algebra, and they found that most of the results concerning graded Clifford algebras have analogues in the case of graded skew Clifford algebras, provided the appropriate non-commutative geometric data is defined. More recently, T. Cassidy and the speaker defined a ``skew'' version of classical Clifford algebras, and related such algebras to graded skew Clifford algebras. Indeed, just as (classical) Clifford algebras are the Poincaré-Birkhoff-Witt (PBW) deformations of exterior algebras, skew Clifford algebras are the $Z_2$-graded PBW deformations of quantum exterior algebras.