In this paper, I provide an overview of the expanding use of predictive policing and the narratives backing its implementation . Within the ongoing debate on the use of algorithmic predictions in law enforcement, my point is above all a critique of conventional criticisms, mostly inspired by a privacy-centred approach that focuses on the risks of profiling as the ultimate benchmark for assessing predictive methods . Through practical examples and surveys into the criminological rationalities fuelling predictive initiatives, I argue how, although relevant, this dimension falls short of grasping the technical and theoretical complexities of predictive policing, which frequently leads to inadequate regulatory responses . The need for a holistic approach reflects the key role played by predictive policing in the deployment of neoliberal governance and, in particular, in redefining the traditional relationship between private and public powers in the security provision chain . Against this backdrop, radical criminology is called to a relentless debunking of dominant rhetoric, in view of which I sketch the basis for a necessary future attunement between the materialist sociology of penal control and the critical theory of police power .