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Despite the recent success of large-scale deep learning, these systems still fall short in terms of their reliability and trustworthiness. They often lack the ability to estimate their own uncertainty in a calibrated way, encode meaningful prior knowledge, avoid catastrophic failures, and also reason about their environments to avoid such failures. Since its inception, Bayesian deep learning (BDL) has harbored the promise of achieving these desiderata by combining the solid statistical foundations of Bayesian inference with the practically successful engineering solutions of deep learning methods. This was intended to provide a principled mechanism to add the benefits of Bayesian learning to the framework of deep neural networks. However, compared to its promise, BDL methods often do not live up to the expectation and underdeliver in terms of real-world impact. This is due to many fundamental challenges related to, for instance, computation of approximate posteriors, unavailability of flexible priors, but also lack of appropriate testbeds and benchmarks. To make things worse, there are also numerous misconceptions about the scope of Bayesian methods, and researchers often end up expecting more than what they can get out of Bayes. By bringing together researchers from diverse communities, such as machine learning, statistics, and deep learning practice, in a personal and interactive seminar environment featuring debates, round tables, and brainstorming sessions, our Dagstuhl Seminar "Rethinking the Role of Bayesianism in the Age of Modern AI" (24461) has discussed these questions from a variety of angles and charted a path for future research to innovate, enhance, and strengthen meaningful real-world impact of Bayesian deep learning.