  We extend Massey products from cohomology to differential cohomology via
stacks, organizing and generalizing existing constructions in Deligne
cohomology. We study the properties and show how they are related to more
classical Massey products in de Rham, singular, and Deligne cohomology. The
setting and the algebraic machinery via stacks allow for computations and make
the construction well-suited for applications. We illustrate with several
examples from differential geometry and mathematical physics.
