a corner stone of the theory of random matrices is wigner's semi-circle law, obtained in the 1950s, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random hermitian matrix with iid (upper diagonal) entries follows the semi-circle law. the non-hermitian case is the famous circular law conjecture, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random matrix with iid entries is uniform in the unit circle.\\ despite several partial results (ginibre-mehta, girko, bai, edelman, gotze-tykhomirov, pan-zhu etc) the conjecture remained open for more than 50 years. in 2008, t. tao and i confirmed the conjecture in full generality. i am going to give an overview of this proof, which relies on rather surprising connections between various fields: combinatorics, probability and theoretical computer science.