This paper proposes and discusses the use of composite marginal like- lihoods for Bayesian inference. This approach allows one to deal with complex statistical models in the Bayesian framework, when the full likelihood - and thus the full posterior distribution - is impractical to compute or even analytically un- known. The procedure is based on a suitable calibration of the composite likelihood that yields the right asymptotic properties for the posterior probability distribu- tion. In this respect, an attractive technique is offered for important settings that at present are not easily tractable from a Bayesian perspective, such as, for in- stance, multivariate extreme value theory. Simulation studies and an application to multivariate extremes are analysed in detail