Testing and code reviews are known techniques to improve the quality
and robustness of software.  Unfortunately, the complexity of modern
software systems makes it impossible to anticipate all possible
problems that can occur at runtime, which limits what issues can
be found using testing and reviews.  Thus, it is of interest to
consider autonomous self-healing software systems, which can
automatically detect, diagnose, and contain unanticipated problems
at runtime.  Most research in this area has adopted a model-driven
approach, where actual behavior is checked against a model specifying
the intended behavior, and a controller takes action when the system
behaves outside of the specification.  However, it is not easy to
develop these specifications, nor to keep them up-to-date as the
system evolves.  We pose that, with the recent advances in machine
learning, such models may be learned by observing the system.
Moreover, we argue that artificial immune systems (AISs) are
particularly well-suited for building self-healing systems, because
of their anomaly detection and diagnosis capabilities.  We present
the state-of-the-art in self-healing systems and in AISs, surveying
some of the research directions that have been considered up to
now.  To help advance the state-of-the-art, we develop a research
agenda for building self-healing software systems using AISs,
identifying required foundations, and promising research directions.