In the first part of this talk, we will see what affine sieve is and the best possible basic result on the subject. In particular, the connection with random walk on $\prod_p{\rm GL}_n(F_p)$ (sometimes called super-strong approximation). In the second part I will report on the new results on random walks on ∏pGLn(Zp) $\prod_p {\rm GL}_n(\mathbb{Z}_p)$.