In this talk, I will discuss about the structure of ideals in enveloping algebras of affine Kac-Moody algebras and explain a proof of the result which states that if U(L) is the enveloping algebra of the affine Lie algebra L and "c" is the central element of L, then any proper quotient of U(L)/(c) by two sided ideals has finite GK dimension and also talk about the applications of the result including the fact that U(L)/(c-\lambda) for non zero \lambda is simple. This talk is based on joint work with Susan J. SIerra.