We review open questions and prospects for progress in ultrahigh-energy cosmic ray (UHECR) research, based on a series of discussions that took place during the `The High-Energy Universe: Gamma-Ray, Neutrino, and Cosmic-ray Astronomy' MIAPP workshop in 2018. Specifically, we overview open questions on the origin of the bulk of UHECRs, the UHECR mass composition, the origin of the end of the cosmic-ray spectrum, the transition from Galactic to extragalactic cosmic rays, the effect of magnetic fields on the trajectories of UHECRs, anisotropy expectations for specific astrophysical scenarios, hadronic interactions, and prospects for discovering neutral particles as well as new physics at ultrahigh energies. We also briefly present upcoming and proposed UHECR experiments and discuss their projected science reach.