This talk will consider several examples of large-scale random systems, such as particles systems with conservation laws, systems of random walks with mutual or self-interaction, the dimer model in Z^d, d>2. Important features of these models are the lack of integrability properties and the presence of long-range correlations, which make their rigorous analysis particularly challenging. The main question is the characterisation of the global properties of such systems, for example the occurrence of a phase transition. We will present an overview.