I overview the work of the Tbilisi school on intuitionistic modal logics of well-founded/scattered structures and its connections with contemporary Theoretical Computer Science. Fixed-point theorems and their consequences are of particular interest.
Litak, T. (2014). Constructive modalities with provability smack. In Outstanding Contributions to Logic (Vol. 4, pp. 187–216). Springer. https://doi.org/10.1007/978-94-017-8860-1_8