Graph-based semi-supervised learning (SSL) algorithms have gained increased attention in the last few years due to their high classification performance on many application domains. One of the widely used methods for graph-based SSL is the Gaussian Fields and Harmonic Functions (GFHF), which is formulated as an optimization problem using a Laplacian regularizer term with a fitting constraint on labeled examples. Such a method and its variations were effectively applied on many fields of machine learning, such as active learning and dimensionality reduction. In this paper, we provide an overview on the GFHF algorithm, focusing on its regularization framework, convergence analysis, out-of-sample extension, scalability, and active learning. We also provide an experimental analysis on inductive SSL in order to show that we can effectively classify out-of-sample examples using the GFHF algorithm without the necessity of using kernel expansions.