The Dagstuhl Seminar on 16481 (New Directions for Learning with Kernels and Gaussian Processes) brought together two principal theoretical camps of the machine learning community at a crucial time for the field. Kernel methods and Gaussian process models together form a significant part of the discipline's foundations, but their prominence is waning while more elaborate but poorly understood hierarchical models are ascendant. In a lively, amiable seminar, the participants re-discovered common conceptual ground (and some continued points of disagreement) and productively discussed how theoretical rigour can stay relevant during a hectic phase for the subject.