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Let f be a polynomial with complex coefficients and x be a special point of the special fiber. We will recall the notion of Milnor fiber of f at x. Using arcs with origin at x, Denef and Loeser introduced a motive S_{f,x} in a Grothendieck ring of varieties with action of roots of unity. This motive encodes all the additive and multiplicative invariants of the Milnor fibration of f at x and its monodromy. In particular, we can recover the monodromy zeta function or the spectrum of f at x. For that reason, it is called motivic Milnor fiber. There exists other motives which encode invariants of global Milnor fibrations or more generally of nearby cycles of f. If we have time we will present them at the end of the talk.

The talk is a part of the conference on singularities and motivic integration.