Let zeta(s) be the Riemann-zeta function. It has long been known that for n an even natural number, the values of zeta(n) are all irrational (even transcendental). However, the question for odd n remained unsolved until around 30 years ago. At a conference held on June 1978, R. Apery stunned his audience with a very involved proof that zeta(3) is irrational. The proof was subsequently simplified by F. Beukers. In this talk we will gradually ease into this proof by means of related proofs of the irrationality of log 2 and zeta(2).