This report documents the program and the outcomes of Dagstuhl Seminar 22061 "Logic and Random Discrete Structures". The main topic of this seminar has been the analysis of large random discrete structures, such as trees, graphs, or permutations, from the perspective of mathematical logic. It has brought together both experts and junior researchers from a number of different areas where logic and random structures play a role, with the goal to establish new connections between such areas and to encourage interactions between foundational research and different application areas, including probabilistic databases.