The smallest Euler number achievable by a smooth surface of general type is $3$. The first example was constructed by David Mumford, who actually constructed a fake projective plane, which is a smooth surface with the same Betti numbers as but not biholomorphic to the projective plane. The purpose of the talk is to explain a classification scheme of Gopal Prasad and myself on fake projective planes, which eventually leads to complete classification with the help of Donald Cartwright and Tim Steger. Moreover, a surface of general type with Euler number 3 but not a fake projective plane, namely Cartwright-Steger surface was constructed. It turns out that these are all the examples that exist. Some historical facts, some analytic results needed and some further developments would be mentioned as well.