Abstract: The Fourier and Fourier-Stieltjes algebras are function algebras formed from the representation theory of groups. Since their introduction, they've been widely studied as their own objects and for their connections to various other algebraic constructions and properties of groups. Separately, groups can be generalized into another algebraic object known as a 'groupoid'. Groupoids have seen their own rise in popularity recently. This talk, based on my recently defended dissertation, joins these two fields together and examines one way to define Fourier and Fourier-Stieltjes algebras over groupoids and will detail several functorial results pertaining to these objects.