Retail electricity markets require development to ensure efficient and equitable pass through of wholesale electricity costs to customers. Customer engagement has been heralded as a concept to improve the wholesale-to-retail link, better harness flexible demand loads and co-ordinate distributed renewable generation and storage. This study reviews the state-of-the-art customer engagement trends in retail electricity markets, and in doing so, it first establishes a definition of customer engagement in the context of retail electricity markets. Second, the paper identifies that literature on customer engagement revolves around three key strategic themes, namely ‘Customer Focus’, ‘Tariff Design’ and ‘Innovation’. Third, the paper systematically provides a comprehensive review of these customer engagement strategies in retail electricity markets. Finally, the study identifies the technical, market and social requirements to deliver an innovative retail electricity market structure to decarbonise society. This paper's crucial and novel policy recommendation is that integrating market mechanisms and technology (i.e. cross-linking across the three customer engagement strategy themes) is required to ensure robust and efficient retail electricity market operation as society advances to a net zero economy. The study concludes with the establishment of eight future research directions of customer engagement for retail electricity market design.