Sieves are an important tool in analytic number theory. In a typical sieve problem, one is given a list of p-adic conditions for all primes p, and the challenge is to count the number of integers which satisfy all these p-adic conditions. In this talk we present some versions of sieves for varieties whose rational points are equidistributed, and give applications to counting rational points in thin sets. This is joint work with Tim Browning.