The common statistical models for network valued datasets (implicitly) assume vertex exchangeability, a multi-dimensional analogue to de Finetti style exchangeability that provides a natural formalisation of the requirement that the labels of a random graph carry no information about its structure. This seemingly innocuous assumption implies that the corresponding networks are densely connected: a property that rarely holds for real-world networks of practical interest. I will discuss recent work generalising these dense exchangeable models to the sparse graph regime. The key ingredient is a novel notion of exchangeability for graphs based on a point process representation of networks. In particular, I will cover the construction of the new models through a de Finetti style representation theorem, the sampling design naturally associated with the model class, and estimation of the models via a graph analogue to the empirical distribution function.