In task-parallel programs, diversee activities can take place concurrently, and communication and synchronization patterns are complex and not easily predictable. Previous work has identifiedcompositionalityas an important design principle for task-parallel programs. In this article, we discuss alternative approaches to the realization of this principle, which holds that properties of program components should be preserved when those co ponents are composed in parallel with other program components. We review two programming languages, Strand and Program Composition Notation, that support compositionality via a small number of simple concepts, namely, monotone operations on shared opbects, a uniform addressing mechanism, and parallel composition. Both languages have been used extensively for large-scale application development, allowing us to provide an informed assessment of both their strengths and their weaknesses. We observe that while compositionality simplifies development of complex applications, the use of specialized languages hinders reuse of existing code and tools and the specification of domain decomposition strategies. This suggests an alternative approach based on small extensions to existing sequential languages. We conclude the article with a discussion of two languages that realized this strategy.