In the mammalian brain, cortical interneurons (INs) are a highly diverse group of cells. A key neurophysiological question concerns how each class of INs contributes to cortical circuit function and whether specific roles can be attributed to a selective cell type. To address this question, researchers are integrating knowledge derived from transcriptomic, histological, electrophysiological, developmental, and functional experiments to extensively characterise the different classes of INs. Our hope is that such knowledge permits the selective targeting of cell types for therapeutic endeavours. This review will focus on two of the main types of INs, namely the parvalbumin (PV) or somatostatin (SOM)-containing cells, and summarise the research to date on these classes.