  Rare meson decays are among the most sensitive probes of both heavy and light
new physics. Among them, new physics searches using kaons benefit from their
small total decay widths and the availability of very large datasets. On the
other hand, useful complementary information is provided by hyperon decay
measurements. We summarize the relevant phenomenological models and the status
of the searches in a comprehensive list of kaon and hyperon decay channels. We
identify new search strategies for under-explored signatures, and demonstrate
that the improved sensitivities from current and next-generation experiments
could lead to a qualitative leap in the exploration of light dark sectors.
