Cortical networks are composed of glutamatergic excitatory projection neurons and local GABAergic inhibitory interneurons that gate signal flow and sculpt network dynamics. Although they represent a minority of the total neocortical neuronal population, GABAergic interneurons are highly heterogeneous, forming functional classes based on their morphological, electrophysiological, and molecular features, as well as connectivity and in vivo patterns of activity. Here we review our current understanding of neocortical interneuron diversity and the properties that distinguish cell types. We then discuss how the involvement of multiple cell types, each with a specific set of cellular properties, plays a crucial role in diversifying and increasing the computational power of a relatively small number of simple circuit motifs forming cortical networks. We illustrate how recent advances in the field have shed light onto the mechanisms by which GABAergic inhibition contributes to network operations. Tremblay et al. review our current knowledge of the diversity of neocortical GABAergic inhibitory interneurons and discuss how the intrinsic properties of interneuron subtypes contribute to specific computational properties within various circuit motifs formed between inhibitory and excitatory neurons.