As a result of works of many mathematicians using representation theory, automorphic forms, exponential sums, etc it was known that the Cayley graphs Cay(G (mod n), S (mod n)) forms a family of sparse highly connected graphs aka expanders, where G is an arithmetic group. In the past decade, it was proved, in certain cases, that what is crucial is the Zariski closure of G and not its arithmeticity. In this talk, first I will survey the recent advances in the subject. Then I will briefly present my work in progress where I give the necessary and sufficient condition under which {Cay(G (mod q), S (mod q))} form a family of expanders as q varies among the powers of primes.