This talk explores the different roles played by asynchrony in asynchronous iterative methods. The first part examines asynchronous variants of classical first- and second-order linear iterations, the Chebyshev method, and multigrid algorithms, highlighting their efficiency and fault tolerance in parallel computing environments. The second part introduces the fundamentals of reinforcement learning (RL) and discusses the use of asynchronous update schemes for state-value estimation when searching for optimal policies. In settings where the state space is extremely large and cannot be fully enumerated, asynchronous methods naturally concentrate computational effort on the regions of the state space that are most frequently visited.