Hybrid systems: reachability visited and revisited

effort during the last 10-15 years. Around 1995 this domain seemed
to be well-explored: all interesting questions (except several
particular cases) proved to be undecidable.

After a survey of these results I will discuss recent progress in
the domain. I will describe some "postmodern" developments
witnessing of richness and complexity of the area, including the
following questions:
- beyond Church's thesis;
- noise and decidability;
- between decidable and undecidable;
- acceleration for continuous systems.

I will conclude by a comparison between the verification-based
approach to computability in the continuous domain and those of
computable analysis and algebraic complexity.