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This paper is a survey of work done on $\mathbb{N}$-graded Clifford algebras(GCAs) and $\mathbb{N}$-graded \textit{skew} Clifford algebras (GSCAs)\cite{VVW, SV, CaV, NVZ, VVe1, VVe2}. In particular, we discuss the hypothesesnecessary for these algebras to be Artin Schelter-regular \cite{AS, ATV1} andshow how certain `points' called, point modules, can be associated to them. Wemay view an AS-regular algebra as a noncommutative analog of the polynomialring. We begin our survey with a fundamental result in \cite{VVW} that isessential to subsequent results discussed here: the connection between pointmodules and rank-two quadrics. Using, in part, this connection the authors in\cite{SV} provide a method to construct GCAs with finitely many distinctisomorphism classes of point modules. In \cite{CaV}, Cassidy and Vancliffintroduce a quantized analog of a GCA, called a graded \textit{skew} Cliffordalgebra and Nafari et al. \cite{NVZ} show that most Artin Schelter-regularalgebras of global dimension three are either twists of graded skew Cliffordalgebras of global dimension three or Ore extensions of graded Cliffordalgebras of global dimension two. Vancliff et al. \cite{VVe1, VVe2} go a stepfurther and generalize the result of \cite{VVW}, between point modules andrank-two quadrics, by showing that point modules over GSCAs are determined by(noncommutative) quadrics of $\mu$-rank at most two.

Graded Clifford Algebras and Graded Skew Clifford Algebras and Their Role in the Classification of Artin-Schelter Regular Algebras