Graph-based Semi-Supervised Learning (SSL) methods have had empirical success in a variety of domains, ranging from natural language processing to bioinformatics. Such methods consist of two phases. In the first phase, a graph is constructed from the available data; in the second phase labels are inferred for unlabeled nodes in the constructed graph. While many algorithms have been developed for label inference, thus far little attention has been paid to the crucial graph construction phase and only recently has the importance of the graph construction for the resulting success in label inference been recognized. In this report, we shall review some of the recently proposed graph construction methods for graph-based SSL. We shall also present suggestions for future research in this area.