Let p(n) denote the usual partition function. If q>3 is prime, then let d(q) mod q be the residue class for which 24 d(q)=1 mod q. If q=5, 7, or 11, then Ramanujan proved that p(qn + d(q)) =0 mod q (*) for every integer n. It is widely believed that there are no other primes q for which (*) holds. In a different direction, Newman conjectured that if q is prime, then for every r mod q there are infinitely many integers n for which p(n) = r mod q. Here we present the latest on these conjectures.