Celtic face a difficult task in the Champions League after the draw for the group stage paired them with holders AC Milan, Benfica and Shakhtar Donetsk.
Thirty-two clubs enter the competition at the group stage
Rangers also face a tough task, against Barcelona, Lyon and Stuttgart.
Chelsea have been drawn with Valencia, whom they defeated at the quarter-final stage of last season's competition.
Liverpool take on Porto, Marseille and Besiktas, while Manchester United face a rematch with Roma and Arsenal play four teams they have not met before.
Arsenal were drawn in Group H along with Steau Bucharest, Slavia Prague and Sevilla.
Gunners managing director Keith Edelman said: "I think it is the first time we have had a draw in which we have never played any of the teams we have been drawn against."
Manchester United, drawn in Group F, played Roma in a quarter-final tie last season, thrashing the Italian side 7-1 in the second-leg at Old Trafford to complete an aggregate 8-3 victory.
It's an extremely tough draw for us
Rangers manager Walter Smith
However, the tie was marred by violence during the first match in Rome.
"We need to do our homework but I am not concerned at all," said United chief executive David Gill.
"We need to make sure that the match is remembered for what happens on the pitch, not off it.
"We must make sure that our fans travel in comfort and safety. It is a new season and we are looking forward to it."
Celtic have also been drawn against opposition they met in last season's competition, the Scottish club running eventual champion's Milan close as they battled for a place in the quarter-finals.
The tie was goalless after the first leg at Celtic Park, before Gordon Strachan's team lost 1-0 in extra-time in the second leg at the San Siro.
Celtic chairman Brian Quinn said: "It is a tough group, we have played them all recently and we know their quality.
"But we qualified last year from a very tough group so I am not down-hearted at all."
Scottish rivals Rangers, however, face an extremely tough task against Spanish giants Barca, French champions Lyon and Stuttgart, who won the German title last season for the first time in 15 years.
The Champions League is the elusive competition for us and there is a big determination
Chelsea chief executive Peter Kenyon
"It's an extremely tough draw for us but there is a great element of glamour about it," said manager Walter Smith.
"There is a great standard of teams and it is clearly going to be very hard for us. We have some huge games to look forward to."
Chelsea defeated Valencia to reach last season's semi-final, with Michael Essien scoring in the last minute of the second-leg in Spain to secure a 3-2 aggregate victory.
Jose Mourinho's team also face Schalke and Rosenborg in Group B.
"Overall I think there are no easy groups but got to be satisfied with that," said Chelsea chief executive Peter Kenyon.
"We have been to the semi-finals two times in the last four years. It is the elusive competition for us and there is a big determination. There is a huge expectation at Chelsea to move to the next stage."
Liverpool chief executive Rick Parry was pleased with his team's draw, which includes a trip to Turkey to play Besiktas.
"We are happy enough," said Parry. "We have happy memories of Istanbul.
"We have proved we are capable of beating anyone on our day and we have a better squad this season."
Draw for the 2007/08 Champions LeagueBritish teams in bold and the top seeds in CAPITALS