Gaudin model is a completely integrable quantum spin chain assigned to a semisimple Lie algebra $\mathfrak g$. In fact it is a degeneration of the $XXX$ model. The famous Feigin-Frenkel-Reshetikhin constuction interprets it as some quantum Hamiltonian reduction such that that the phase space is some space of conformal blocks of the corresponding affine Lie algebra $\hat{\mathfrak g}$ on the critical level and the Hamiltonians come from the center of the universal enveloping algebra. The center at the critical level is naturally identified with the algebra of polynomial functions on the space of opers on the formal punctured disk with respect to the Langlands dual group $G^L$
(roughly, the space of gauge equivalence classes of connections in a principal $G^L$-bundle with some transversality condition). This allows us to treat the spectra of Gaudin algebras on g-modules as some subsets in the space of opers. Bethe Ansatz conjecture describes these subsets for irreducible finite-dimensional g-modules, as spaces of global opers on the projective line with prescribed singularities and with trivial monodromy representation. I will give a sketch of a proof of this conjecture.