Non-classical logics have been proposed in a number of domains, including constructive mathematics, quantum mechanics, and natural language semantics. In this talk, I will identify a base logic beneath some of these non-classical logics that I suggest has a certain fundamental status. I will give an introduction to the proof theory and semantics of this "fundamental logic." I will then discuss the problem of how to think about conditionals in light of the proof-theoretic and semantic story for fundamental logic. The paper associated with the talk is available at https://arxiv.org/abs/2207.06993.