Bioprinting technologies have been extensively studied in literature to fabricate three-dimensional constructs for Tissue Engineering applications. However, very few examples are currently available on clinical trials using bioprinted products, due to a combination of technological challenges (i.e., difficulties in replicating the native tissue complexity, long printing times, limited choice of printable biomaterials) and regulatory barriers (i.e., no clear indication on the product classification in the current regulatory framework). In particular, quality control solutions are needed at different stages of the bioprinting workflow (including pre-process optimization, in-process monitoring, and post-process assessment) to guarantee a repeatable product which is functional and safe for the patient. In this context, machine learning algorithms can be envisioned as a promising solution for the automatization of the quality assessment, reducing the inter-batch variability and thus potentially accelerating the product clinical translation and commercialization. In this review, we comprehensively analyse the main solutions that are being developed in the bioprinting literature on quality control enabled by machine learning, evaluating different models from a technical perspective, including the amount and type of data used, the algorithms and the performance measures. Finally, we give a perspective view on current challenges and future research directions on using these technologies to enhance the quality assessment in bioprinting.