Robert Lewandowski scored twice as Barcelona breezed to a 5-0 win against Young Boys at Estadi Olimpic Lluis Companys.
Goals from Lewandowski, Raphinha and Inigo Martinez put the game to bed by half-time, with Lewandowski grabbing a fourth early in the second half and Mohamed Camara putting through his own net late on.
Victor Boniface scored the only goal of the game, having had an earlier effort disallowed, as Bayer Leverkusen edged to a 1-0 victory over AC Milan.
Hakan Calhanoglu's first-half opener was added to after the interval by Marko Arnautovic and Lautaro Martinez before Mehdi Taremi struck from the spot as Inter Milan brushed aside Red Star Belgrade 4-0.
Sporting Lisbon claimed a 1-1 draw at PSV Eindhoven after Daniel Braganca cancelled out Jerdy Schouten's goal for the Dutch side.
Abdallah Sima (above) scored in either half as Brest thrashed Red Bull Salzburg 4-0, while Stuttgart and Sparta Prague drew 1-1.
Kai Havertz and Bukayo Saka scored first-half goals as Arsenal claimed a statement win in the Champions League after seeing off French champions Paris St Germain 2-0.
Havertz headed home after 20 minutes following a pinpoint cross from Leandro Trossard, who was allowed to ghost virtually unchallenged from the halfway line to the edge of the PSG area.
Stand-in captain Saka doubled Arsenal's advantage with 10 minutes of the first half remaining courtesy of a free-kick from close to the touchline, which sailed past the unsighted Gianluigi Donnarumma.
Manchester City also eased to their first victory in Europe's elite club competition this season as they brushed Slovan Bratislava aside 4-0 in Slovakia, having drawn with Inter Milan last month.
Early goals from Ilkay Gundogan and Phil Foden put them in command before Erling Haaland's 42nd goal in 41 appearances in the competition and another from substitute James McAtee added the gloss.
Celtic's unbeaten start to the campaign was emphatically ended as they crashed to a 7-1 defeat at Borussia Dortmund.
Daizen Maeda cancelled out Emre Can's penalty but Karim Adeyemi's excellent first-half hat-trick plus Serhou Guirassy's spot-kick left Celtic trailing 5-1 at half-time. Guirassy scored again before Felix Nmecha completed a one-sided rout.
Watch Liverpool v Bologna in the Champions League on Wednesday from 7.30pm on RTÉ2 and RTÉ Player. Follow a live blog on rte.ie/sport and the RTÉ News app. Digital highlights of games available from Thursday morning.
Watch the FAI Cup semi-finals, Bohemians v Derry City on Friday from 7.35pm and Drogheda United v Wexford on Sunday from 2.45pm. Both game on RTÉ2 and RTÉ Player with live blog on rte.ie/sport and the RTÉ News app
Watch Shamrock Rovers v Shelbourne in the League of Ireland on Sunday from 5.15pm on RTÉ2 and RTÉ Player. Follow a live blog on RTÉ.ie/sport and the RTÉ News app
