The development of models of computation induces the development of technology and natural sciences and vice versa. Current state of the art of technology and sciences, especially networks of concurrent processes such as Internet or biological and sociological systems, calls for new computational models. It is necessary to extend classical Turing machine model towards physical/ natural computation. Important aspects are openness and interactivity of computational systems, as well as concurrency of computational processes. The development proceeds in two directions - as a search for new mathematical structures beyond algorithms as well as a search for different modes of physical computation that are not equivalent to actions of human executing an algorithm, but appear in physical systems in which concurrent interactive information processing takes place. The article presents the framework of infocomputationalism as applied on computing nature, where nature is an informational structure and its dynamics (information processing) is understood as computation. In natural computing, new developments in both understanding of natural systems and in their computational modelling are needed, and those two converge and enhance each other.