We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics and neuroinformatics depends on the adequate models of computation. In this article we first present the current state of the art through systematization of existing models and mechanisms, and outline basic structural framework of computation. We argue that defining computation as information processing, and given that there is no information without (physical) representation, the dynamics of information on the fundamental level is physical/ intrinsic/ natural computation. As a special case, intrinsic computation is used for designed computation in computing machinery. Intrinsic natural computation occurs on variety of levels of physical processes, containing the levels of computation of living organisms (including highly intelligent animals) as well as designed computational devices. The present article offers a typology of current models of computation and indicates future paths for the advancement of the field; both by the development of new computational models and by learning from nature how to better compute using different mechanisms of intrinsic computation.