Additive manufacturing of continuous reinforced polymer is currently a focus topic in the composite manufacturing industry as it represents a viable solution to satisfy the requirements of high volume production and automation that could facilitate expanding the use of composite materials and meet sustainability goals. Nevertheless, several challenges need to be addressed to increase the quality standards to match those of parts manufactured by standard composite processing routes. Specifically, consolidation issues appear to be the determining factor which hold the technology back. The present review paper analyses current consolidation techniques utilised in additive processing of composites and identifies the most promising current and future manufacturing technologies capable of complying with stringent sustainability, quality and cost standards.