The long-standing Foulkes' Conjecture asserts that a certain difference of plethythms of complete homogeneous symmetric functions is Schur-positive. Vessenes has stated a Generalized Foulkes' Conjecture. I will explain these two conjectures and some work done on them. I will also introduce my own generalization, which I have reason to believe is more natural and perhaps easier to prove. All of these conjectures about symmetric functions specialize to conjectures about q-binomial coefficients, which have a nice combinatorial interpretation.