Rees algebras are of special interest in algebraic geometry and commutative algebra since they describe the blowing up of the spectrum of a ring along the subscheme defined by an ideal. The Rees algebra of an ideal can also be viewed as a quotient of a polynomial ring. If I is an ideal of a ring R, we denote the Rees algebra of I by R[I t], and we can represent R[I t] as S/J where S is a polynomial ring over R. The ideal J is called the defining ideal of R[I t]. Finding generators of J is difficult and crucial for better understanding R[I t]. Many authors have worked to gain better insight into these generators in special classes of ideals, such as those with special height, special embedding dimension and so on.