Finite W-algebras are certain associative algebras associated to a complex semisimple
Lie algebra g and a nilpotent element e of g.<br> In the special case e = 0, the W-algebra is
the universal enveloping algebra. On the other hand, the Yangian Y (glN), introduced
by <br> 
Drinfeld, is a deformation of the universal enveloping algebra for the polynomial
current Lie algebra glN[x]. <br> <br>

In 2004, Brundan and 
Kleshchev found various parabolic presentations for the Yangian Y (glN), 
which can be used to define certain <br> algebras called 
shifted Yangians. Moreover, 
they gave explicitly 
a remarkable realization of finite W-algebras as a quotient of shifted Yangians.
<br> <br>
The goal of this talk is to explain the above connections and our generalization to
the superalgebra case.