Since its emergence in the 1960s, array notation has been valued as a powerful abstraction to program in a compact form and to represent parallelism. The main theme of this presentation is that today there is much to be gained by expanding the use of array notation. That the notation can be profitably used for a wide range of problem domains, programming paradigms, and to take advantage of multiple architectural features. Indeed, array notation can be used not only for numerical linear algebra but also for different classes of symbolic computing including the implementation of graph algorithms. Extensive use of array notation would not only improve productivity, but also reduce the overhead of interpretation of dynamic languages, and facilitate the representation of shared memory parallelism, distributed memory communication operations, and locality. Furthermore, the introduction of new operators and compiler strategies would enable the use of the notation in new directions including irregular and asynchronous computations.