The Russian scientists have first discussed Sputnik V with EMA (EU's medicine agency) 5 days ago: https://www.msn.com/en-xl/europe/top-stories/russia-files-sp... ; Hungary, which is part of the EU, has already given the vaccine emergency authorization. However, vaccination in Hungary is lagging behind its neighbors Austria and Romania due low levels of trust (in the Russian vaccine) and general antivaxx sentiment. The Chinese have not discussed their vaccines or filed for marketing authorisation in the EU.

The development, evaluation, approval and monitoring process is described in detail here: https://www.ema.europa.eu/en/human-regulatory/overview/publi...

And on to of that Russia and China are much further behind in the rollout to their own population than the EU itself - see https://ourworldindata.org/grapher/covid-vaccination-doses-p...