Abstract: Given a variety X a natural question to ask is whether it is birational to projective space. In general, this is quite a very hard question to answer. We restrict ourselves to a subclass of objects known as algebraic tori. It turns out that a slightly weaker notion related to rationality can be "cleanly" understood in terms of the character lattice for a given torus. I will give some background to state this result and then discuss the work that has been done on the rationality question for algebraic tori.