This report documents the program and the outcomes of Dagstuhl Seminar 16031 “Well Quasi-Orders in Computer Science”, the first seminar devoted to the multiple and deep interactions between the theory of Well quasi-orders (known as the Wqo-Theory) and several fields of Computer Science (Verification and Termination of Infinite-State Systems, Automata and Formal Languages, Term Rewriting and Proof Theory, topological complexity of computational problems on continuous functions). Wqo-Theory is a highly developed part of Combinatorics with ever-growing number of applications in Mathematics and Computer Science, and Well quasi-orders are going to become an important unifying concept of Theoretical Computer Science. In this seminar, we brought together several communities from Computer Science and Mathematics in order to facilitate the knowledge transfer between Mathematicians and Computer Scientists as well as between established and younger researchers and thus to push forward the interaction between Wqo-Theory and Computer Science.