Graphs are commonly used to represent complex networks, such as the internet or biological systems. The structure of a graph can be inferred by clustering vertices based on dissimilarity measures correlated with the underlying graph-distances. For example, internet hosts can be clustered by measured latencies or traffic correlations and genes can be clustered according to responses to varied experimental conditions. These clusters reveal the structure of the underlying graph; e.g., internet routing or functional pathways in biological systems. This tutorial talk will discuss theory, methods, and applications of graph-learning based on clustering. Learning with missing or incomplete data, which is the norm in practice, will be a key theme in the discussion. The theory draws from ideas in statistical learning, spectral and subspace clustering, and matrix completion. The main concepts will be illustrated with examples from communication and biological network inference problems.