In the vast expanse and scope of fluid mechanics, thermal and species transport, droplets have carved out an important niche for themselves. These microscopic fluid entities, bounded to shape by surface tension and/or interfacial forces, play important roles in variant capacities in the physical world, biological systems as well as man-made technological applications. Thereby, understanding of droplet dynamics is an essential area in research and development. To add to the complexity of interfacial thermofluidic transport in droplets, presence of electric and/or magnetic fields yields interesting and rich physics to the problem. Additionally, such field-induced transport in droplets has found applications in several systems, ranging from macro- to microscale. Consequently, research on the physics of thermofluidic transport in the presence of electromagnetic stimulus has gained wide attention in the academic community. The present article discusses the present status of research, development and knowledge base on the topic. The physics of the problem, scope and extent of work realized by the academic community till date, potential applications and future directions have been discussed in an effort to provide a comprehensive review. The article shall be able to provide the readers a precis of the research and developmental work in the field thus far and acquaint them with an idea of the path ahead.