The Coates-Sinnott Conjecture was formulated in 1974 as a K-theory analogue of Stickelberger's Theorem. For a finite abelian extension $E/F$ of number fields and any integer $n\geq 2$, this conjecture constructs an element in terms of special values of the (equivariant) L-function of $E/F$ at $1-n$ to annihilate the even Quillen K-group $K_{2n-2}(O_E)$ of associated ring of integers $O_E$ over the group ring $\mathbb{Z}[Gal(E/F)]$. In this talk after describing the precise formulation of the conjecture we present the recent results. Part of this is a joint work with Manfred Kolster.