Let X be a connected CW-complex and let X_n denote its n-skeleton. A pointed map f: X ® Y is called a phantom map if its restriction to each X_n is null-homotopic. Non-trivial phantom maps are often elusive creatures that are hard to detect. There is one homotopy invariant, however, which was defined by Brayton Gray. In this talk, I will discuss the properties of the Gray invariant, a conjecture concerning the finiteness of the Gray index of phantom maps between finite type spaces and its connection to sub-functors of lim¹, and finally some applications.