This Dagstuhl Seminar intends to bring together machine learning researchers working on algorithm development, mathematicians interested in provable guarantees, and practitioners applying embedding methods in biology, chemistry, humanities, social science, etc. Our aim is to bring together the world's leading experts to (i) survey the state of the art; (ii) identify critical shortcomings of existing methods; (iii) brainstorm ideas for the next generation of methods; and (iv) forge collaborations to help make these a reality.