Valhalla is an open-source routing engine for OpenStreetMap data. Besides route calculation it provides distance matrices, isochrones, elevation sampling, map matching and tour optimisation, and it supports multimodal routes combining driving, walking, cycling and public transport. Its tiled data structure keeps memory use low and allows offline routing and regional extracts. Developers use it through an HTTP API, a C++ library, or Python and Node.js bindings. It is delivered as software that you build from source or run as a Docker image on your own infrastructure.
Valhalla is released under the MIT licence and developed as a community project on GitHub; it began as a component of Mapzen's mapping products, and Mapzen ceased operations in 2018. No vendor stands behind it, so the project has no corporate headquarters or foreign parent. Because you run the engine yourself, you decide where it is hosted and which data it processes, which makes it a suitable building block for a European routing service. A public demo server run by FOSSGIS e.V. is available under fair-use limits.