Unconventional computation emerged as a response to a series of technological and societal challenges. The main source of these challenges is the expected collapse of Moore’s law. It is very likely that the existing trend of building faster digital information processing machines will come to an end. This chapter provides a broad philosophical discussion of what might be needed to construct a theoretical machinery that could be used to understand the obstacles and identify the alternative designs. The key issue that has been addressed is simple to formulate: given a physical system, what can it compute? There is an enormous conceptual depth to this question and some specific aspects are systematically discussed. The discussion covers digital philosophy of computation, two reasons why rocks cannot be used for computation are given, a new depth to the ontology of number, and the ensemble computation inspired by recent understanding of the computing ability of living cell aggregates.