  In this paper we present recent results on the computation of skein modules
of 3-manifolds using braids and appropriate knot algebras. Skein modules
generalize knot polynomials in $S^3$ to knot polynomials in arbitrary
3-manifolds and they have become extremely essential algebraic tools in the
study of 3-manifolds. In this paper we present the braid approach to the
HOMFLYPT and the Kauffman bracket skein modules of the Solid Torus ST and the
lens spaces $L(p,1)$ and $S^1\times S^2$.
