Providing assurances for self-adaptive systems is challenging. A primary underlying problem is uncertainty that may stem from a variety of different sources, ranging from incomplete knowledge to sensor noise and uncertain behavior of humans in the loop. Providing assurances that the self-adaptive system complies with its requirements calls for an enduring process spanning the whole lifetime of the system. In this process, humans and the system jointly derive and integrate new evidence and arguments, which we coined perpetual assurances for self-adaptive systems. In this paper, we provide a background framework and the foundation for perpetual assurances for self-adaptive systems. We elaborate on the concrete challenges of offering perpetual assurances, requirements for solutions, realization techniques and mechanisms to make solutions suitable. We also present benchmark criteria to compare solutions. We then present a concrete exemplar that researchers can use to assess and compare approaches for perpetual assurances for self-adaptation.