Bayern have taken an early lead in Group A, with Copenhagen and Galatasaray playing out a 2-2 draw in the other match in the section, leaving Man United at the bottom.
In Group B, Arsenal opened with a 4-0 victory over PSV Eindhoven at the Emirates Stadium, while Lens and Sevilla could not be separated, with the two teams playing out a 1-1 draw in Spain.
Napoli and Real Madrid both won in Group C, with the former beating Braga 2-1, while the latter recorded a 1-0 victory over Union Berlin courtesy of a last-gasp Jude Bellingham strike.
Red Bull Salzburg lead Group D, meanwhile, having opened with a 2-0 victory over Benfica, while Inter Milan and Real Sociedad played out a 1-1 draw in their contest in Spain.
Group E is currently led by Feyenoord, who beat Celtic 2-0, while Lazio drew 1-1 with Atletico Madrid, with the standout moment coming in the final seconds, when the Italian side's goalkeeper Ivan Provedel headed an equaliser.
Paris Saint-Germain lead Group F, having beaten Borussia Dortmund 2-0, while Newcastle United survived an onslaught to claim a point in a goalless draw away to AC Milan.
RB Leipzig and Manchester City were both winners in Group G, meanwhile, with the former beating Young Boys 3-1, while the latter overcame Red Star Belgrade by the same scoreline in Manchester.
Barcelona are the early leaders in Group H, thumping Royal Antwerp 5-0 in their section opener, while Porto are also on three points, having beaten Shakhtar Donetsk 3-1.
Here, Sports Mole selects its standout XI from the first game week of this season's Champions League group stages.
DEFENCE
Newcastle's Nick Pope and Union Berlin's Frederik Ronnow are unfortunate to miss out between the sticks, but the position just had to go to Ivan Provedel, who headed a 95th-minute leveller for Lazio against Atletico.
Provedel became the first goalkeeper to score in a Champions League match for 13 years and only the fourth overall, so he simply had to be included in the team of the week.
There are three defenders in this XI, with Giovanni Di Lorenzo one of those, having excelled in Napoli's win over Braga, finding the back of the net in the 46th minute of the match, in addition to boasting a pass success rate of 88% during an excellent all-round performance.
Mohamed Simakan also makes it, with the 23-year-old playing an important role in Leipzig's win over Young Boys, scoring in the early stages, while he won four aerial duels during a dominant display in the middle.
The defensive side of the team is completed by Achraf Hakimi, who was on the scoresheet in PSG's win over Dortmund, but it was his overall performance that impressed the most, boasting a pass success rate of 87%, in addition to completing three dribbles and winning three tackles.
MIDFIELD
Jude Bellingham made it six goals in six appearances for Real Madrid this season with the winner against Union Berlin on Wednesday. The 20-year-old was again the dominant force for the hosts, having four shots, winning two aerial duels and completing 59 of his 66 passes during a brilliant performance.
Martin Odegaard also sails into the midfield due to his excellent performance against PSV, with the Norway international on the scoresheet in North London, while he boasted a pass success rate of 91%, completed three dribbles and had three shots, starring once again for the Gunners.
Jamal Musiala did not score against Man United on Wednesday, but he was the best player on the pitch, providing a brilliant assist for Serge Gnabry's goal, while he was a constant menace between the lines, rarely relinquishing control of the football.
The midfield is completed by Ilkay Gundogan, who provided an assist during Barcelona's 5-0 win over Antwerp. The Germany international has been an excellent signing for Xavi's side, and he was a class act in the middle on Tuesday, finishing with a pass success rate of 94%, setting the tempo for the hosts.
ATTACK
Galeno makes the attack, having excelled in Porto's 3-1 win over Shakhtar on Tuesday; the 25-year-old was the star of the show, scoring twice in the opening 15 minutes before setting up Mehdi Taremi for his side's third, and Shakhtar just could not deal with his movement in the final third of the field.
Joao Felix is also included due to his showing against Antwerp; much has been made of the Portugal international's loan move to Barcelona from Atletico, but he has started his Camp Nou career impressively, and he scored a brace and came up with an assist in Tuesday's Champions League encounter.
The attack is rounded off by Julian Alvarez, who was Man City's best player in the victory over Red Star Belgrade. The Argentine netted twice to turn the match around early in the second period, and his overall game was outstanding, having eight shots in total, three successful dribbles and completing 53 of his 59 passes.
SPORTS MOLE'S CHAMPIONS LEAGUE TEAM OF THE WEEK
Sports Mole's Champions League team of the week (3-4-3): Provedel; Di Lorenzo, Simakan, Hakimi; Gundogan, Bellingham, Odegaard, Musiala; Galeno, J Alvarez, Felix