Title: Vanishing cycles and Fourier transform in motivic integration: first steps towards motivic microlocal geometry. Abstract: We shall first review our construction (with Denef) of a version of motivic vanishing cycles and present some recent results obtained with Guibert and Merle. We will then present a recent construction of motivic integration, developed in joint work with Raf Cluckers, which is based on cell decomposition. This construction allows in particular to develop a Fourier calculus. We shall conclude the talk by giving some recent applications of this motivic Fourier calculus.