This tutorial paper considers the problem of reconstructing Genetic Regulatory Networks (GRNs) from gene expression measurements. Among various modeling frameworks that have been proposed for these biological systems, we focus on PieceWise Affine (PWA) models because of their ability to capture both the switching behavior of genes and the continuous dynamics of molecule concentrations. PWA models of GRNs have a special structure that must be preserved by the identification process. In the paper, we discuss the new challenges that this constraint raises in the field of hybrid identification. As an example, we summarize recently proposed methods for detecting switches in gene expression profiles and for reconstructing multiple PWA models consistent with the data. We also present the results obtained by applying these algorithms to synthetic data produced by PWA models of the GRN governing the carbon starvation response in E. coli.