The reigning champions Real Madrid were 3-1 winners over Stuttgart, while Juventus overcame PSV Eindhoven, Aston Villa thumped Young Boys and Sporting Lisbon edged past Lille on the opening night.
Also on Tuesday, Liverpool recorded a 3-1 victory over AC Milan, before the action continued on Wednesday, with Celtic putting five goals past Slovan Bratislava.
Sparta Prague beat Red Bull Salzburg 3-0, while Paris Saint-Germain edged past Girona, and Borussia Dortmund were 3-0 winners over Club Brugge.
There were two goalless draws on Wednesday, meanwhile, with Bologna holding Shakhtar Donetsk, and Manchester City failing to find a route past Inter Milan.
On Thursday, Bayer Leverkusen thumped Feyenoord 4-0, while Benfica and Brest were 2-1 winners over Red Star Belgrade and Sturm Graz respectively.
Monaco beat 10-man Barcelona 2-1, while the same scoreline also allowed Atletico Madrid to collect all three points against RB Leipzig, but Atalanta BC and Arsenal could not be separated in Italy, with Gunners goalkeeper David Raya making a stunning double save in that encounter.
Here, Sports Mole selects its Champions League Team of the Week from the opening set of fixtures in the league phase of the competition.
DEFENCE
David Raya's eye-catching double save against Atalanta will live long in the memory, with the Spain international keeping out a spot kick from Mateo Retegui before incredibly denying the 25-year-old from the rebound when it looked certain that he would be heading his side into the lead.
For that moment, Raya simply had to be included between the sticks, but his overall performance was outstanding, with the 29-year-old calm and composed throughout the contest.
Due to the volume of matches, a number of strong performers had to be left out of this XI, and it was particularly hard to pick the defence, with Liverpool's Virgil van Dijk one who was unlucky not to be included.
Vanderson's two assists against Barcelona earn him the right-back spot, with the Brazilian, who is said to be a transfer target for the Catalan outfit in excellent form. Meanwhile, on the opposite side, there had to be a position for Josko Gvardiol, who was outstanding in Man City's 0-0 draw with Inter.
Antonio Rudiger was on the scoresheet in Real Madrid's 3-1 success over Stuttgart, while he also won three aerial duels and boasted a pass success rate of 91%; he is included alongside Lucumi, with the 26-year-old winning five aerial duels and making five tackles in Bologna's goalless draw with Shakhtar.
MIDFIELD
There simply had to be a spot in central midfield for Arne Engels, with the 21-year-old in excellent form during Celtic's 5-1 win over Slovan Bratislava. Engels set up his side's opening goal of the match before scoring himself early in the second period, while he had four shots and made six tackles during an all-action performance.
Youri Tielemans is also included due to his role in Villa's 3-0 success over Young Boys. The Belgian made the breakthrough in the 27th minute of the contest, and he then turned provider for fellow central midfielder Amadou Onana to register in the latter stages. Tielemans was at his best on Tuesday, completing 52 of his 56 passes during an excellent European performance.
The third and final midfield spot goes to Jamal Musiala, who was in stunning form for Bayern against Dinamo Zagreb on Tuesday night. The German provided two assists in his team's 9-2 win, while he had four shots and managed four successful dribbles in Munich, with the visitors simply unable to deal with him.
ATTACK
There are two more Bayern players in the XI, with Harry Kane unsurprisingly leading the line due to his four goals in Bayern's nine-goal showing on Tuesday night. The England captain was at his dominant best in the Champions League fixture, having eight shots in total, while he also managed 30 accurate passes.
Michael Olise was another standout performer for the Bundesliga giants, netting twice on his debut in the competition, while the 22-year-old, who represented France at the Paris Olympics, had two successful dribbles and won two aerial duels during an all-action display in Munich.
The final spot in the XI is awarded to the outstanding Florian Wirtz, who struck a brace in Leverkusen's 4-0 win over Feyenoord on Thursday night. The 21-year-old finished with a pass success rate of 87%, meanwhile, and he was a constant problem for Feyenoord due to his movement and trickery.
Jamie Gittens is unfortunate to miss out following his brace off the bench for Dortmund, while Antoine Griezmann is also certainly worth a mention, with the Frenchman scoring once and providing one assist in Atletico's narrow home success over RB Leipzig.
SPORTS MOLE'S CHAMPIONS LEAGUE LEAGUE TEAM OF THE WEEK
Sports Mole's Champions League Team of the Week (4-3-3): Raya; Vanderson, Lucumi, Rudiger, Gvardiol; Tielemans, Musiala, Engels; Olise, Kane, Wirtz