Provable security is the science of building cryptographic protocols out of building blocks in a sound way. Namely, one proves the only way to break a protocol is to break one of the building blocks. But does every secure protocol have such a proof? What if we can't find one? This talk will introduce the concept of "idealized models,'' which are models of computation created by cryptographers to address this issue. We will describe what idealized models are and why they are used. Then, we will describe our on-going line of research aimed at better analyses in such models, as well as transitioning the proofs to do without idealized models when possible. Such results give greater assurance in the security of many widely-used cryptographic protocols. The talk will be high-level and will not assume previous knowledge of cryptography.