Recently, a number of frameworks were proposed to extend interface theory to the domains of single-processor and distributed real-time systems. This paper unifies some of these approaches and proves properties like refinement and independent implementability. We also explicitly state the requirements to a framework for these properties to be fulfilled. Further, a new notion of adaptive interfaces is introduced that supports the design by providing mechanisms for propagating system constraints, such as (end-to-end) delays, available computing and communication resources, buffer spaces, and energy. Guarantees and assumptions on interfaces are not any longer static but adapt according to the system environment. This can be used to answer synthesis questions at design time or to adapt system parameters to changing environment requirements at run-time. The applicability of the presented framework is proven by adapting it to a number of different real-time analysis models. Categories and Su...