Abstract. We will discuss some relatively recent work concerning asymptotic and exact formulas for the irreducible characters of the symmetric group. Two different asymptotic results, due to Vershik-Kerov and Biane, will be given. The work of Biane is related to Kerov's "universal character polynomial" which Kerov defined in a lecture shortly before his death. A new formula for irreducible characters of rectangular shape yields some information about Kerov's universal character polynomial.