Extending the original approach to motivic integration, Cluckers and Loeser developed a model theoretical notion of motivic integration. In this talk we will introduce their motivic integration and the transfer principle obtained from it. The construction of this form of motivic integration relies heavily on a version of cell-decomposition in the Denef-Pas language. We will show how the original notion of cell decomposition yields quantifier elimination for certain henselian valued fields and in fact one can deduce Ax–Kochen–Ersov results from this quantifier elimination. In a similar fashion, Cluckers‘ and Loeser’s motivic integration leads to a motivic version of transfer principle of the Ax–Kochen–Ersov transfer principle. More precisely, this transfer principle allows the transferral of equalities of p-adic integrals between certain fields of characteristic zero and those of positive characteristic with isomorphic residue fields. In particular this includes equalities of p-adic integrals on F_p((t)) and Q_p for all but finitely many primes p.