In this paper, we show how the questions of what is computable and what is feasibly computable can be viewed from the viewpoint of physics: what is computable within the current physics? what is computable if we assume -- as many physicists do -- that no final physical theory is possible? what is computable if we consider data processing, i.e., computations based on physical inputs? Our physics-based analysis of these questions leads to some unexpected answers, both positive and negative. For example, we show that under the no-physical-theory-is-perfect assumption, almost all problems are feasibly solvable -- but not all of them.