Conformal prediction (CP) has emerged as a cutting-edge framework in modern statistics, providing prediction intervals with finite-sample frequentist coverage guarantees. Work has suggested that it can be used to impart frequentist validity to Bayesian procedures (Wasserman, 2011; Fong and Holmes, 2021; Hoff, 2023), motivating deeper investigation into such a frequentist–Bayesian hybrid. After surveying existing ideas, this talk will present the general Bayesian CP framework in both its full and split variants. For simple key examples, we will present equivalent analytic solutions that bypass the computational complexity of full CP. Empirical analyses will illustrate how prior specification affects both coverage and efficiency, showcasing the complementary role of the two paradigms, jointly striving for a nearly-optimal balance between frequentist validity and Bayesian efficiency.