In the rapidly advancing field of multi-modal machine learning (MMML), the convergence of multiple data modalities has the potential to reshape various applications. This paper presents a comprehensive overview of the current state, advancements, and challenges of MMML within the sphere of engineering design. The review begins with a deep dive into five fundamental concepts of MMML:multi-modal information representation, fusion, alignment, translation, and co-learning. Following this, we explore the cutting-edge applications of MMML, placing a particular emphasis on tasks pertinent to engineering design, such as cross-modal synthesis, multi-modal prediction, and cross-modal information retrieval. Through this comprehensive overview, we highlight the inherent challenges in adopting MMML in engineering design, and proffer potential directions for future research. To spur on the continued evolution of MMML in engineering design, we advocate for concentrated efforts to construct extensive multi-modal design datasets, develop effective data-driven MMML techniques tailored to design applications, and enhance the scalability and interpretability of MMML models. MMML models, as the next generation of intelligent design tools, hold a promising future to impact how products are designed.