openrouteservice is a set of open-source geo-services operated by HeiGIT gGmbH. Through a single interface it offers routing for cars, trucks, bikes, walking, hiking and wheelchairs, isochrones (reachability areas), time-distance matrices, geocoding with Pelias, points of interest, elevation data based on SRTM, and route optimisation based on VROOM. The services use OpenStreetMap data and, according to the website, are free to use. You can call them through the public API or run them yourself.
HeiGIT gGmbH is based in Heidelberg, Germany, and is the data controller for the service. The software is open source and dual-licensed under GPL-3.0 and LGPL-3.0, and the README recommends Docker for self-hosting, which allows an organisation to keep routing requests on its own infrastructure. The privacy policy states that data handled by service providers may be transferred to countries outside the EU under contractual safeguards.