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. (Thi Hanh VO, May 31) The second part includes several summation methods of divergent series. The definitions of the summation methods are accompanied by a plethora of examples of summations of famous divergent series. Several theorems allow to compare the strength of the various summation methods. Furthermore, we will present regularization via the analytical continuation of the zeta function, with a particular focus on the derivation of the result 1+2+3+…=-1/12. We conclude by giving other values of the zeta-function in terms of the Bernoulli numbers.