There is a folklore conjecture that there are infinitely
many primes p such that p+2 is also prime.
This conjecture is still open.  However, in the last two years,
spectacular progress has been made to show that there are
infinitely many primes p such that p+h is also prime with
1< h < 247.  We will discuss the history of this problem
and explain the new advances in sieve theory that have led
to these remarkable results.  We will also highlight what we may
expect in the future.