Summary: This paper examines the limitations of Turing Machines as a complete model of computation, and presents several models that extend Turing Machines. Dynamic interaction of clients and servers on the Internet, an infinite adaptation from evolutionary computation, and robots sensing and acting are some examples of areas that cannot be properly described using Turing Machines and algorithms. They require new models of computation going beyond Turing Machines. We refer to such new models as superTuring models of computation. Three superTuring models of computation, namely Interaction Machines, the \(\pi\)-calculus and the \(\lambda\)-calculus are presented and explained, focussing on why they are better for the solution of computational problems. We expect that superTuring computation will become the central programming paradigm in the future.