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Software architectures have the potential to substantially improve the development and evolution of large, complex, multi-lingual, multi-platform, long-running systems. However, in order to achieve this potential, specific architecture-based modeling, analysis, and evolution techniques must be provided. This paper motivates and presents one such technique: a type theory for software architectures, which allows flexible, controlled evolution of software components in a manner that preserves the desired architectural relationships and properties. Critical to the type theory is a taxonomy that divides the space of subtyping relationships into a small set of well defined categories. The paper also investigates the effects of large-scale development and off-the-shelf reuse on establishing type conformance between interoperating components in an architecture. An existing architecture is used as an example to illustrate a number of different applications of the type theory to architectural modeling and evolution.