Yes, Liverpool FC has won several European tournaments throughout their history.

The most prestigious of these is the UEFA Champions League, which Liverpool has won six times. Their first victory came in 1977, when they defeated Borussia Mönchengladbach 3-1 in the final. They went on to win the tournament again in 1978, beating Club Brugge 1-0 in the final.

After a long drought, Liverpool won the Champions League again in 2005 in what is widely regarded as one of the greatest finals in the history of the competition. They were trailing 3-0 to AC Milan at halftime, but managed to mount a stunning comeback to win on penalties. They won the tournament again in 2019, defeating Tottenham Hotspur 2-0 in the final.

Liverpool has also won the UEFA Cup (now known as the Europa League) three times. They won the tournament in 1973, 1976, and 2001. In addition, they have won the UEFA Super Cup four times, in 1977, 2001, 2005, and 2019.

Overall, Liverpool is one of the most successful clubs in European football history, with a total of nine major European trophies to their name.