  This is a review of our previous works (some of them joint with B. Feigin and
N. Reshetikhin) on the Gaudin model and opers. We define a commutative
subalgebra in the tensor power of the universal enveloping algebra of a simple
Lie algebra g. This algebra includes the hamiltonians of the Gaudin model,
hence we call it the Gaudin algebra. It is constructed as a quotient of the
center of the completed enveloping algebra of the affine Kac-Moody algebra g^
at the critical level. We identify the spectrum of the Gaudin algebra with the
space of opers associated to the Langlands dual Lie algebra of g on the
projective line with regular singularities at the marked points. Next, we
recall the construction of the eigenvectors of the Gaudin algebra using the
Wakimoto modules over g^ of critical level. The Wakimoto modules are naturally
parameterized by Miura opers (or, equivalently, Cartan connections), and the
action of the center on them is given by the Miura transformation. This allows
us to relate solutions of the Bethe Ansatz equations to Miura opers and
ultimately to the flag varieties associated to the Langlands dual Lie algebra
of g.
