The main aim of the review is to address the importance of computations in the analyses of manufacturing processes during efficient materials design, tool design, and process design. Initially, the evolution of computations in manufacturing industries is highlighted. The applications of different computational approaches like numerical simulations, analytical modeling, soft computing, etc. in solving metal forming and joining problems are presented. Though there are several manufacturing processes, metal forming and joining applications are included in the present work. The later part of the review is about green manufacturing and sustainability, their relation with computations and manufacturing education. The green manufacturing and sustainability practices in different industries/fields (like automotive, machining, steel, food processing, computers, electronics) are tabulated. The significance of computations in green manufacturing and sustainability issues are described with a few examples from available literature. The last part of the work is about improving the awareness of green and sustainability concepts through manufacturing education. In this, the possible ways of modifying the present course content of ‘manufacturing technology’ in under-graduate education are suggested, by giving importance to green and sustainability concepts. The role of computations in manufacturing education is summarized finally.