The composite part industry is currently dominated by thin-section geometries. However, thick composites gain interest in many applications where monolithic parts are required, such as foils, wind mill root blades, and so forth. Their manufacturing continues to face major challenges due to the phenomena at play during infusion and curing stages, whose complexity intensifies as components thickness increases. At the same time, the composite industry must comply with increasingly stringent quality standards and near-zero waste requirements, making the task of selecting optimal design parameters highly complex. In this article, the main challenges concerning the infusion and curing of thick thermosetting composites are presented, and potential mitigation strategies are critically reviewed. Finally, emerging trends in the field, including variability modeling, machine learning for process optimization, process monitoring, novel manufacturing methods, and the development of new materials, are identified and discussed. Highlights: Enhanced resin flow and optimized injection reduce infusion defects occurrence. Optimized cure cycles have been extensively used to mitigate cure defects. Established strategies can be improved through ML and stochastic simulations. New processing strategies could redefine the composite manufacturing industry.