Random simple and multigraph models based on exchangeable random measures, sometimes named graphex processes or generalised graphon models, have recently been proposed as a flexible class of sparse random graph models. This class of models can be seen as a generalisation of the popular graphon models. I will present this class of models, discuss some of their asymptotic properties, in particular the asymptotic behaviour of the degree distribution and of the clustering coefficients. I will also present some particular parametric models within this class and their use for discovering latent communities in sparse real-world networks.