Regulatory circuits are found at the basis of all non-trivial dynamical properties of biological networks. More specifically, positive circuits are involved in the generation of multiple differentiated states, whereas negative circuits can generate cyclic or homeostatic behaviours. These notions are briefly reviewed, from initial biological formulations to mathematical formalisations, further encompassing their application to the design of synthetic regulatory systems. Finally, current challenges for the analysis of increasingly complex regulatory networks are indicated, as well as prospects for our understanding of development and evolution.