A polyomino is a shape made by connecting a certain number of equal sized squares, each joined together with at least on other square along an edge. The question of whether a region in the plane can be perfectly tiled using polyominoes drawn from a finite set of polyominoes is a well-established tiling problem. This talk will give an overview of necessary conditions for such a tiling to exist using combinatorial group-theoretic invariants from Conway and Lagarias' paper.