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The basis of a problem-oriented view of software-intensive systems is the recognition of three fundamental roles to be played by models in a development: R, the requirement; W, the given properties of the problem world; and S, the specification of the machine's behaviour at its interface with the problem world. These are (ideally) related by the entailment S,W |= R. Decomposition of a problem into subproblems is analogous (but not identical) to decomposition of a system into components. A subproblem has R, W and S, its machine interacting with a subset of the problem world. Conceptually, subproblems are initially considered in isolation, composition concerns being deferred. Composition of subproblems involves relationships among all three of their models R, W and S; in general different subproblems use different models, even of the same parts of the problem world. Problem world properties are not in general compositional. Relationships among subproblems, and hence among their models, may be complex.