The vision of project WASP SELF-HEALING is a world where software-intensive systems are reliable despite the openness and unpredictability of the environment. Today, the best-of-breed of software engineering techniques cannot achieve both at the same time. We know how to build ultra-reliable software in stable and closed environments such as a nuclear power plant. We know how to build software that runs in ultra-open environments, such as Android mobile applications that run on millions on different ultra-heterogeneous devices. But we do not know how to achieve both in conjunction and this is a problem: most systems today, from peer-to-peer systems à la Bitcoin to autonomous transportation systems must be reliable yet evolve in a fundamentally open and unpredictable world. The goal of project WASP SELF-HEALING is to devise a conceptual, theoretical and algorithmic framework for enabling the construction of software that is reliable in open and unpredictable environments.