Kernel methods have become ubiquitous across science and engineering. For more than two decades, radial basis function finite difference (RBF-FD) methods have provided flexible, high-order discretizations for partial differential equations on complex domains and manifolds. More recently, Gaussian Process (GP) perspectives have opened new directions in nonlinear solvers, uncertainty quantification, and operator learning, while retaining the potential for very high-order convergence. This four-slot minisymposium brings together researchers from these complementary communities to exchange ideas, identify common mathematical structure, and develop new connections between kernel-based numerical methods and kernel-based learning.