This critical and scoping review essay analyses digital labour markets where labour-intensive services are traded by matching requesters (employers and/or consumers) and providers (workers). It focuses on digital labour markets which allow the remote delivery of electronically transmittable services (i.e. Amazon Mechanical Turk, Upwork, Freelancers, etc.) and those where the matching and administration processes are digital, but the delivery of the services is physical and requires direct interaction. The former broad type is called Online Labour Markets (OLMs) and is potentially global. The latter broad type is termed Mobile Labour Markets (MLMs) and is by definition localised. The essay defines and conceptualises these markets proposing a typology which proves to be empirically valid and heuristically useful. It describes their functioning and the socio-demographic profiles of the participants, reviews their economic and social effects, discusses the possible policy implications, and concludes with a research agenda to support European level policy making. It alternates the discussion of ‘hard’ findings from experimental and quasi-experimental studies with analysis of ‘softer’ issues such as rhetorical discourses and media ‘hyped’ accounts. This triangulation is inspired by, and a tribute to, the enduring legacy of the work of Albert O. Hirschman and his view that ideas and rhetoric can become endogenous engines of social change, reforms, and policies. This essay tries to disentangle the rhetoric with available empirical evidence in order to enable a more rational debate at least in the discussion of policies, if not in the public arena.