The concept of circular economy (CE) is becoming progressively popular with academia, industry, and policymakers, as a potential path towards a more sustainable economic system. Information and communication technology (ICT) systems have influenced every aspect of modern life and the CE is no exception. Cutting-edge technologies, such as big data, cloud computing, cyber-physical systems, internet of things, virtual and augmented reality, and blockchain, can play an integral role in the embracing of CE concepts and the rollout of CE programs by governments, organizations, and society as a whole. The current paper conducts an extensive academic literature review on prominent ICT solutions paving the way towards a CE. For the categorization of the solutions, a novel two-fold approach is introduced, focusing on both the technological aspect of the solutions (e.g., communications, computing, data analysis, etc.), and the main CE concept(s) employed (i.e., reduce, reuse, recycle and restore) that each solution is the most relevant to. The role of each solution in the transition to CE is highlighted. Results suggest that ICT solutions related to data collection and data analysis, and in particular to the internet of things, blockchain, digital platforms, artificial intelligence algorithms, and software tools, are amongst the most popular solutions proposed by academic researchers. Results also suggest that greater emphasis is placed on the “reduce” component of the CE, although ICT solutions for the other “R” components, as well as holistic ICT-based solutions, do exist as well. Specific important challenges impeding the adoption of ICT solutions for the CE are also identified and reviewed, with consumer and business attitude, economic costs, possible environmental impacts, lack of education around the CE, and lack of familiarization with modern technologies being found among the most prominent ones.