Falkon is a Python library for large-scale kernel ridge regression and logistic regression, leveraging Nyström approximation and preconditioned conjugate gradient to scale to billions of points. It provides a scikit-learn-like API (fit/predict) with GPU acceleration via custom CUDA/cuBLAS/cuSOLVER kernels and optional KeOps integration for on-the-fly kernel-vector products. The library includes hyperparameter optimization through differentiable objectives (LOOCV, GCV, Nyström compression) with gradient-based solvers, out-of-core operations for GPU memory overflow, and sparse tensor support. Benchmark infrastructure compares Falkon against GPyTorch, GPflow, and EigenPro on datasets like Higgs, TIMIT, MillionSongs. The codebase is well-tested with CI/CD for CPU/GPU builds and pre-built wheels for multiple PyTorch/CUDA combinations. While the core library is production-grade, some benchmark scripts are one-off and a few modules have TODO comments or limited platform support (Linux-only, Windows untested).