The theory of graph limits considers the convergence of sequences of graphs with a diverging number of vertices. From an applied perspective, it aims to represent very large networks conveniently. In this talk, I will give an introduction and overview of this active area of research. In particular, I will present the well-established limit theory for dense graph sequences (graphons) underlying the combinatorial, probabilistic and analytic point of view. My talk will conclude by discussing other limit notions for graphs and more complicated combinatorial structures such as hypergraphs.