Reconstructing gene regulatory networks from high-throughput measurements represents a key problem in functional genomics. It also represents a canonical learning problem and thus has attracted a lot of attention in both the informatics and the statistical learning literature. Numerous approaches have been proposed, ranging from simple clustering to rather involved dynamic Bayesian network modeling, as well as hybrid ones that combine a number of modeling steps, such as employing ordinary differential equations coupled with genome annotation. These approaches are tailored to the type of data being employed. Available data sources include static steady state data and time course data obtained either for wild type phenotypes or from perturbation experiments. This review focuses on the class of autoregressive models using time course data for inferring gene regulatory networks. The central themes of sparsity, stability and causality are discussed as well as the ability to integrate prior knowledge for successful use of these models for the learning task at hand.