This volume results from two programs that took place at the Institute for Mathematical Sciences at the National University of Singapore: Aspects of Computation - in Celebration of the Research Work of Professor Rod Downey (21 August to 15 September 2017) and Automata Theory and Applications: Games, Learning and Structures (20-24 September 2021). The first program was dedicated to the research work of Rodney G. Downey, in celebration of his 60th birthday. The second program covered automata theory whereby researchers investigate the other end of computation, namely the computation with finite automata, and the intermediate level of languages in the Chomsky hierarchy (like context-free and context-sensitive languages). This volume contains 17 contributions reflecting the current state-of-art in the fields of the two programs.