The defending champions Real Madrid were shocked by CSKA Moscow in Russia while other teams continued their impressive run in the competition.
There are contenders for the UEFA Player of the Week award and it will be a close contest because three stars scored a hat-trick in their respective matches.
Here are the four contenders for the UEFA Player of the week
1. Eden Dzeko (Roma)
The Bosnian international was instrumental to Roma's first win in this season's competition against visiting Vitoria Plzen.
The former Manchester City striker scored a hat-trick in Roma's 5-0 win which put them in contention for qualification in Group G.
Dzeko is a viable contender for the UEFA Player of the Week after posting a man-of-the-match performance for his team.
2. Paulo Dybala (Juventus)
Juventus ran ragged of Swiss side Young Boys in their second group match and the Bianconeri recorded a comfortable win without their talisman Cristiano Ronaldo.
But it was Paulo Dybala who ran the show on the night scoring all three goals at the Allianz Stadium.
The Argentine is also another contender for the best performer in the matchday 2 round of matches.
3. Neymar (PSG)
Paris Saint-Germain finally won their first Champions League match of the season after losing 3-2 to Liverpool at Anfield.
However Neymar opened his account in the competition with a hat-trick in PSG's 6-1 win to Red Belgrade at Parc Des Princes.
The 27-year-old scored two fantastic free kicks which could earn him UEFA's best performing player for matchday 2.
4. Lionel Messi (Barcelona)
The Barcelona star man picked up from where he stopped as La Blaugrana defeated Tottenham 4-2 in an entertaining fixture played at the Wembley Stadium.
The charismatic Argentine scored two sublime goals beating Hugo Loris on two occasions in the easiest of fashions.
The 31-year-old could be rewarded with another award after emerging the winner in the first round of matches.