Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as biology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project aims to answer many fundamental questions about large, random hypergraphs, to close this gap. As well as obtaining these answers, expected outcomes of the project include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.