Our talk concentrates on summation and regularization methods of divergent series. Particular focus will be put on the famous regularization of the divergent series 1+2+3+… to the value of -1/12, which is of uttermost importance in modern physics. The talk splits into two sessions. The first session will be an introductory part, whereas the technical details will be given in the second session. (Jill Marie-Anne ECKER, May 17) The introductory part contains an historical overview on divergent series. This includes the treatment of divergent series by mathematicians of the 18 th century, such as Euler, Leibniz or Bernoulli. Moreover, we will show the importance of divergent series in modern physics such as quantum field theory and string theory.