Dark sectors and their signatures in Kaon physics

I review the set of theoretical ideas motivating experimental searches of light physics beyond the Standard Model. Specifically, I give examples of very weakly interacting candidates that can be probed in direct detection experiments. I then discuss a possibility of probing such states in the high-intensity kaon experiments by looking at the rare and radiate decay modes. The interesting modes to pursue include K ^± → π ^± + missing energy, K ^± → π ^± π ⁰ e ⁺ e ^-, as well as Dalitz and double-Dalitz decays of π ⁰.