By avoiding discretization, the Generalized Method of Moment based on a Continuum of moment conditions (CGMM) permits to effciently use the information content of a continuum moment restrictions. When the moment restrictions are deduced from a characteristic function, the CGMM has the potential to achieve the maximum likelihood efficiency. This chapter reviews the theory underlying the CGMM procedure, discusses the properties of the CGMM estimator and presents numerical algorithms for its implementation. An empirical application is proposed where a Variance Gamma model is fitted to the monthly increments of the USD/GBP exchange rates. We find that the variance forecasts inferred from the Variance Gamma model are of poor quality. A model that specifies the variance as a dependent process should deliver better forecasts. JEL Classification: C00, C13, C15