Khintchine's theorem is a key result in Diophantine approximation. Given a positive non-increasing function f defined over the integers, it states that the set of real numbers that are f-approximable has zero or full Lebesgue measure depending on whether the series of terms f(n))_n converges or diverges. I will present a recent work in collaboration with Weikun He and Han Zhang in which we extend Khintchine's theorem to any self-similar probability measure on the real line. The result provides an answer to an old question of Mahler, also asked by Kleinbock-Lindenstrauss-Weiss. The argument involves the quantitative equidistribution of upper triangular random walks on SL_2(R)/SL_2(Z).