Classical sequences of numbers often lead to interesting q-analogues. The most popular among them are certainly the q-integers and the q-binomial coefficients which both appear in various areas of mathematics and physics. It seems that q-analogues of rational numbers have been much less popular so far. With Valentin Ovsienko we recently suggested a notion of q-rationals based on combinatorial properties. The definition of q-rationals naturally extends the one of q-integers and leads to a ratio of polynomials with positive integer coefficients. I will explain the construction and give the main properties. I will mention connections with the combinatorics of posets, cluster algebras, Jones polynomials. Finally I will also present further developments of the theory, in particular I will focus on the notion of q-irrationals and q-unimodular matrices.