Arsenal and Manchester City were handed tough Champions League tasks after the draw for the group stage was made in Monaco.
The Gunners were pitted together with last year's beaten finalists Borussia Dortmund, Marseille and Napoli in Group F.
Manchester City also face a tall order if they are to reach the knockout phase for the first time after being drawn with holders Bayern Munich, CSKA Moscow and Viktoria Plzen in Group D.
Chelsea, who won the competition in 2012, appear to have an easier draw after they were put in Group E alongside Schalke, Basel and Steaua Bucharest.
Manchester United have a long trip to Shakhtar Donetsk and also face German and Spanish opposition in the form of Bayer Leverkusen, Real Sociedad in Group A.
Celtic have possibly the hardest task of all the British teams though after being drawn alongside three former winners Barcelona, AC Milan and Ajax. Neil Lennon will be hoping his charges will be able to repeat their heroics against the Catalan side last year, when they beat Barca 2-1 at Celtic Park.
See how all the action unfolded in our live blog here.
Will Arsenal qualify for the knock-out stages?
The draw in full:
Group A: Manchester United, Shakhtar Donetsk, Bayer Leverkusen, Real Sociedad
Group B: Real Madrid, Juventus, Galatasaray, Copenhagen
Group C: Benfica, Paris St-Germain, Olympiakos, Anderlecht
Group D: Bayern Munich, CSKA Moscow, Manchester City, Viktoria Plzen
Group E: Chelsea, Schalke, Basel, Steaua Bucharest
Group F: Arsenal, Marseille, Borussia Dortmund, Napoli
Group G: Porto, Atletico Madrid, Zenit St Petersburg, Austria Vienna
Group H: Barcelona, AC Milan, Ajax, Celtic