In 1960, Milnor and Novikov proved that the complex cobordism ring is a polynomial ring with one generator in each even dimension.  However, convenient choices for these generators are still unknown.   In this talk, I will discuss the role that smooth projective toric varieties play in this polynomial ring structure.  More specifically, I will present evidence supporting the conjecture that the cobordism class of a smooth projective toric variety can be chosen for each polynomial generator.