Given a simple finite Lie algebra over the complex numbers, we can consider two other Lie algebras attached to it: its Langlands dual Lie algebra and the affine algebra at the critical level. It is a theorem of the nineties, by Feigin and Frenkel, that the center of the completed enveloping algebra of the affine algebra at the critical level is canonically isomorphic to the algebra of functions on the space of Opers on the pointed disk for the Langlands dual Lie algebra. These objects are actually pointwise instances of a more general picture: the space of opers for example enhances to a space which lives over an arbitrary smooth curve that is equipped with a natural factorization structure. This structure is fundamental for the geometric Langlands community: factorization patterns allow for local to global arguments. In this talk, I will explain the construction of the objects mentioned above and elaborate on a joint work with Andrea Maffei in which we prove the factorizable version of the Feigin-Frenkel theorem.