Identifying the complicated patterns of regulatory interactions that control when different genes are active in a cell is a challenging problem, but one essential to understanding how organisms function at a systems level. In this chapter, we will examine the role of computational methods in making such inferences by studying one particularly important version of this problem: the inference of genetic regulatory networks from gene expression data. We will first briefly cover some necessary background on the biology of genetic regulation and technology for measuring the activities of distinct genes in a sample. We will then work through the process of how one can abstract the biological problem of finding interactions among genes into a precise mathematical formulation suitable for computational analysis, starting from very simple variants and gradually working up to models suitable for analysis of large-scale networks. We will also briefly cover key algorithmic issues in working with such models. Finally, we will see how one can transition from simplified pedagogical models to the more detailed, realistic models used in actual research practice. In the process, we will learn about some key concepts in computer science and machine learning, consider how computational scientists think about solving a problem, and see why such thinking has come to play an essential role in the emerging field of systems biology.