Genetic regulatory networks (GRNs) are causal structures which can be represented as large directed graphs. Their inference is a central problem in bioinformatics. Because of the paucity of available data and high levels of associated noise, machine learning is essential to performing good and tractable inference of the underlying causal structure. This chapter serves as a review of the GRN field as a whole, as well as a roadmap for researchers new to the field. It describes the relevant theoretical and empirical biochemistry and the different types of GRN inference. It also describes the data that can be used to perform GRN inference. With this biologically-centred material as background, the chapter surveys previous applications of machine learning techniques and computational intelligence to GRN inference. It describes clustering, logical and mathematical formalisms, Bayesian approaches and some combinations. Each of these is shortly explained theoretically, and important examples of previous research using each are highlighted. Finally, the chapter analyses wider statistical problems in the field, and concludes with a summary of the main achievements of previous research as well as some open research questions in the field.