The main theme of my work is the idea of “Gravity as the square of Yang-Mills” or the so called “double-copy structure of supergravity”. This correspondence is most easily exploited when the super Yang-Mills factors are formulated over the four normed division algebras. A complete understanding of the correspondence requires studying how all global and local symmetries as well as multiplet content of supergravity theories originate from the super Yang-Mills factors. My talk will be a review on recent work on the topic.