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In this thesis, we use logarithmic methods to study motivic objects. Let R bea complete discrete valuation ring with perfect residue field k, and denote byK its fraction field. We give in chapter 2 a new construction of the motivicSerre invariant of a smooth K-variety and extend it additively to arbitraryK-varieties. The main advantage of this construction is to rely only onresolution of singularities and not on a characteristic zero assumption, as didprevious results. As an application, we give a conditional positive answer toSerre's question on the existence of rational fixed points of a G-action on theaffine space, for G a finite l-group. We end the chapter by showing how thelogarithmic point of view that we use in our construction leads to a newunderstanding of the motivic nearby cycles with support of Guibert, Loeser andMerle as a motivic volume.  In chapter 4 we use the theory of logarithmic geometry to derive a newformula for the motivic zeta function via the volume Poincar\'e series. Moreprecisely, we show how to compute the volume Poincar\'e series associated to agenerically smooth log smooth R-scheme in terms of its log geometry, morespecifically in terms of its associated fan in the sense of Kato. This formulayields a much smaller set of candidate poles for the motivic zeta function andseems especially well suited to tackle the monodromy conjecture of Halle andNicaise for Calabi-Yau K-varieties, for which log smooth models appearnaturally through the Gross-Siebert programme on mirror symmetry. We end thechapter by showing how this formula sheds new light on previous resultsregarding the motivic zeta function of a polynomial nondegenerate with respectto its Newton polyhedron, and of a polynomial in two variables.

Motivic Integration and Logarithmic Geometry