In Group A, Ajax recorded a 4-0 victory over Rangers in their section opener, while Napoli stunned last season's finalists Liverpool with a 4-1 victory in Naples.
Atletico Madrid scored in the 11th minute of added time at the end of the 90 to beat Porto 2-1 in their Group B opener, while Club Brugge were 1-0 winners over Bayer Leverkusen in the same section.
As for Group C, Barcelona are the early leaders, having recorded a 5-1 victory over Viktoria Plzen at Camp Nou, while Bayern Munich ran out 2-0 winners over Inter Milan at San Siro.
Tottenham Hotspur opened their Group D campaign with a 2-0 home success over Marseille, while Sporting Lisbon recorded a 3-0 victory against Eintracht Frankfurt in Germany.
In Group E, Dinamo Zagreb ran out 1-0 winners over Chelsea, while AC Milan and Red Bull Salzburg played out a 1-1 draw in the other game in the section.
Real Madrid beat Celtic 3-0 in Glasgow in their Group F opener, but Shakhtar Donetsk are currently at the head of the action, having run out 4-1 winners over RB Leipzig in Germany.
Manchester City lead Group G, meanwhile, having beat Sevilla 4-0 in Spain, while Borussia Dortmund are section courtesy of their 3-0 victory over Copenhagen.
Finally, in Group H, Benfica beat Maccabi Haifa 2-0, while Paris Saint-Germain recorded a 2-1 victory over Juventus in Turin to also start their campaign with all three points.
Here, Sports Mole selects its Champions League Team of the Week from the first set of group matches in the 2022-23 competition.
DEFENCE
At this moment, there is arguably not a better goalkeeper in world football than Thibaut Courtois, and he was again at his best in Real Madrid's win over Celtic on Tuesday. The Belgium international made four smart saves during a dominant performance, while he also boasted a 93% pass rate, completing 40 of his 43 passes, with the stopper putting in a near-perfect display for the reigning champions.
Ahead of him, Man City's Joao Cancelo and Benfica's Alex Grimaldo operate in the full-back positions; the former provided two assists in his side's four-goal success over Sevilla, while the latter set up Rafa for Benfica's opener against Maccabi Haifa before getting his name on the scoresheet four minutes later. Both players were dominant defensively for their respective teams but also hugely impressive going forward.
At centre-back, there is a spot for Jules Kounde, who provided the assist for Franck Kessie to make the breakthrough in the 13th minute of Barcelona's win over Plzen, while he boasted a pass success rate of 93%, in addition to winning five aerial duels and four tackles during an excellent display at Camp Nou.
Dino Peric, meanwhile, is included due to his impressive performance against Chelsea. The 28-year-old played a key role in Dinamo Kiev keeping a clean sheet, winning five aerial duels and making two challenges during a strong display, with Chelsea's attackers finding it difficult to break through the home side's three-man defence.
MIDFIELD
Napoli have two representatives in midfield, with both Piotr Zielinski and Andre-Frank Zambo Anguissa putting in excellent performances in the team's 4-1 win over Liverpool.
Zielinski scored twice and provided an assist against Jurgen Klopp's side, and he was a constant menace to the English outfit throughout the contest, with Napoli proving far too strong over the course of the 90 minutes.
Anguissa got his name on the scoresheet in the 31st minute following an assist from Zielinski, but it was the 26-year-old's overall performance that impressed the most; he won seven tackles, completed two successful dribbles and boasted a pass success rate of 87% in a true all-round midfield display.
The final spot in midfield is taken by Ajax's Steven Berghuis, who played a leading role in his side's 4-0 win over Rangers on Wednesday. The 30-year-old set up Edson Alvarez for the opening goal of the match before getting his name on the scoresheet in the 32nd minute. Berghuis also made three tackles and completed 51 of his 59 passes in Amsterdam, with the home side comfortably winning the midfield battle.
ATTACK
There was a lot of competition for spots in the final third of the field, with Richarlison deserving a special mention due to his brace for Tottenham against Marseille, while Mykhailo Mudryk contributed a goal and two assists in Shakhtar's strong win at Leipzig.
Erling Braut Haaland also scored twice against Sevilla but just misses out, with Ousmane Dembele, Robert Lewandowski and Kylian Mbappe featuring in the final third of the field.
Dembele did not get his name on the scoresheet against Plzen, but he was almost perfect everywhere else, providing two assists, completing six dribbles and generally causing chaos throughout the 90 minutes.
The France international also completed 46 of his 52 passes during a magical display at Camp Nou, with Plzen find it difficult to contain him throughout the game.
Lewandowski is already the leading goalscorer in this season's competition due to his treble on Wednesday night, with the 34-year-old on fire against the Czech outfit, and he has become the first player in Champions League history to score a hat trick for three different teams in the tournament.
The final spot in the XI goes to Mbappe due to his performance against Juventus on Tuesday evening; the France international scored both of his side's goals against the Italian giants, while he had six shots in total during an energetic display. The Old Lady will be pleased that they do not have to face the 23-year-old every week considering the level of performance that he put in during the Group H clash.
SPORTS MOLE'S CHAMPIONS LEAGUE TEAM OF THE WEEK
Sports Mole's Champions League team of the week (4-3-3): Courtois; Cancelo, Peric, Kounde, Grimaldo; Zielinski, Berghuis, Anguissa; Dembele, Lewandowski, Mbappe