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Logic and learning are central to Computer Science, and in particular to AI-related research. Already Alan Turing envisioned in his 1950 "Computing Machinery and Intelligence" paper a combination of statistical (ab initio) machine learning and an "unemotional" symbolic language such as logic. The combination of logic and learning has received new impetus from the spectacular success of deep learning systems. This report documents the program and the outcomes of Dagstuhl Seminar 25061 "Logic and Neural Networks". The goal of this Dagstuhl Seminar was to bring together researchers from various communities related to utilizing logical constraints in deep learning and to create bridges between them via the exchange of ideas. The seminar focused on a set of interrelated topics: enforcement of constraints on neural networks, verifying logical constraints on neural networks, training using logic to supplement traditional supervision, and explanation and approximation via logic. This Dagstuhl Seminar aimed not at studying these areas as separate components, but in exploring common techniques among them as well as connections to other communities in machine learning that share the same broad goals. The seminar format consisted of long and short talks, as well as breakout sessions. We summarize the motivations and proceedings of the seminar, and report on the abstracts of the talks and the results of the breakout sessions.