Champions League holders Real Madrid will face Borussia Dortmund and Tottenham in a difficult group following the draw ceremony in Monaco on Thursday.
Barcelona did not get an easy pass, either, as they were drawn against Juventus, Olympiakos and Sporting CP in Group D.
Aside from Spurs, English teams received slightly easier draws, with Chelsea's matchup with Atletico Madrid among the more challenging matchups, while Liverpool will face Sevilla.
Manchester United will face Benfica, FC Basel and CSKA Moscow in Group A, while Manchester City get Shakhtar Donetsk, Napoli and Feyenoord in Group F.
Teams were drawn into eight groups of four. Clubs from the same national association -- as well as Russian and Ukrainian clubs -- could not be drawn together. The first group games will be played on Sept. 12-13.
Group A: Benfica, Manchester United, FC Basel, CSKA Moscow.
Group B: Bayern Munich, Paris Saint-Germain, Anderlecht, Celtic
Group C: Chelsea, Atletico Madrid, Roma, FK Qarabag
Group D: Juventus, Barcelona, Olympiakos, Sporting CP
Group E: Spartak Moscow, Sevilla, Liverpool, NK Maribor
Group F: Shakhtar Donetsk, Manchester City, Napoli, Feyenoord
Group G: Monaco, FC Porto, Besiktas, RB Leipzig
Group H: Real Madrid, Borussia Dortmund, Tottenham, APOEL Nicosia
Dortmund finished top of their group above Madrid last year, but new coach Peter Bosz still said Real were the most difficult challenge his side could have been drawn against in Group H.
"Real Madrid are the first team that could defend the Champions League title," he said after the draw. "I also saw their [recent Super Cup] matches against Barcelona, and I have to say: That is the absolute top level in football right now.
"For me, it'll be the first time at the Bernabeu, though for most BVB fans it will be a well-known feeling. Against Tottenham, a very strong team, I already played successfully with Feyenoord. And Nicosia rounds off an overall tough group. We're accepting the challenge."
Dortmund CEO Hans-Joachim Watzke told Sky Germany that the club would look to the experience of finishing at the top of an equally tough group in 2012, when BVB went unbeaten against Real Madrid, Ajax and Manchester City before reaching the final.
"No doubt about it. This is the most difficult group," he said. "But we've had that in 2012. We got through a group with Real and Manchester City. Heroes are born in those groups. Sure, we always get Real, and we played Tottenham in Europa League. But we can't pick the teams."
Real Madrid director Emilio Butragueno shrugged off the notion that his club were the favourites to advance, saying "we'll have to be at our best in order to qualify."
"There're a lot of teams that start today with that [favourites] tag," he said. "We're the champions from the last two seasons, we have a great team and a winning spirit. But this competition takes you to the limit in all aspects.
"It depends on a lot of factors and we must think about making it through the group stage. Hopefully we're in the draw for the last 16 as winners of our group."
Tottenham will go up against their former stars Gareth Bale and Luka Modric when they host Real Madrid at Wembley this year, and Spurs forward Harry Kane called the matchups "a good draw."
"You expect to play the best in Europe in the Champions League, and it's exciting for us. We look forward to these games," Kane said. "You want to test yourself against the best, and Real Madrid are the best at the moment.
"It will be interesting to see where we're at and a great test for us against Borussia Dortmund and APOEL as well. I remember the game against Real Madrid at the Lane in 2011. I'm sure Wembley will be packed for the matches, and we can't wait to get started."