The cGAS-STING signalling axis, comprising the synthase for the second messenger cyclic GMP-AMP (cGAS) and the cyclic GMP-AMP receptor stimulator of interferon genes (STING), detects pathogenic DNA to trigger an innate immune reaction involving a strong type I interferon response against microbial infections. Notably however, besides sensing microbial DNA, the DNA sensor cGAS can also be activated by endogenous DNA, including extranuclear chromatin resulting from genotoxic stress and DNA released from mitochondria, placing cGAS-STING as an important axis in autoimmunity, sterile inflammatory responses and cellular senescence. Initial models assumed that co-localization of cGAS and DNA in the cytosol defines the specificity of the pathway for non-self, but recent work revealed that cGAS is also present in the nucleus and at the plasma membrane, and such subcellular compartmentalization was linked to signalling specificity of cGAS. Further confounding the simple view of cGAS-STING signalling as a response mechanism to infectious agents, both cGAS and STING were shown to have additional functions, independent of interferon response. These involve non-catalytic roles of cGAS in regulating DNA repair and signalling via STING to NF-κB and MAPK as well as STING-mediated induction of autophagy and lysosome-dependent cell death. We have also learnt that cGAS dimers can multimerize and undergo liquid-liquid phase separation to form biomolecular condensates that could importantly regulate cGAS activation. Here, we review the molecular mechanisms and cellular functions underlying cGAS-STING activation and signalling, particularly highlighting the newly emerging diversity of this signalling pathway and discussing how the specificity towards normal, damage-induced and infection-associated DNA could be achieved.