Manchester United played very well but couldn't grab a goal in their Champions League match with Inter Milan.
The tie between the Premier League leaders and the top team in Italy was predicted to be very close by experts, but United controlled the game.
Cristiano Ronaldo and Ryan Giggs both had good chances to score, but the match in Milan ended 0-0.
The two teams will meet again in two weeks' time for the second leg of the tie at Old Trafford.
Arsenal were also in action, and they scored an important 1-0 win against another Italian team, Roma.
Striker Robin van Persie netted the winner for the Gunners from the penalty spot, after he'd been fouled inside the area.
Arsenal had a lot of other chances to increase their lead but weren't able to do so, which could make the second leg in Italy very interesting.
On Wednesday the other two Premier League teams in the competition are in action, with Chelsea playing Juventus from Italy and Liverpool taking on Spanish side Real Madrid.