The five British teams in the Uefa Cup all drew unfancied opposition in the first-round proper.
Tottenham face Cypriot side Anorthosis Famagusta, with the opening leg at White Hart Lane, while Bolton take on Macedonian team Rabotnicki.
Bolton are away in the first leg, as are Blackburn Rovers, who play Greek outfit Larissa.
Everton and Aberdeen play Ukrainian opposition, the Toffees taking on Metalist and the Dons Dnipro.
Both Everton and Aberdeen have home ties in the first leg.
Everton chief executive Keith Wyness said: "There is no such thing as an easy draw in Europe.
"Ukraine is a well-known footballing nation but Everton are very focused on taking the club further in Europe this year.
"We hope to be in Europe more consistently."
Aberdeen director of football Willie Miller said: "It is a tough draw.
"Dnipro are second in the Ukraine league, undefeated after seven games but we are looking forward to it and have one tie to get through to the group stage".
Tottenham were defeated at the quarter-final stage last season by eventual winners Sevilla.
"Last year was a big frustration for us," said Tottenham's sporting director Damien Comolli.
We are pleased with the draw - it is not the hardest one we could have had
Blackburn boss Mark Hughes
"Everyone said that the team which won our match would go on to win the competition, and that's what happened."
Bolton are in the Uefa Cup for the second time in three years - and boss Sammy Lee said: "The next chapter of our European adventure takes us to Macedonia against Rabotnicki.
"They are an unknown quantity and we will do our homework near the time."
But Blackburn boss Mark Hughes was happy with his team's draw, which sees them travel to Greece.
"We are pleased with the draw and it is not the hardest one we could have had," said Hughes.
"Zagreb was the team in our section I think everybody would have wanted to avoid.
"The trip to Greece will be difficult because they usually have a vociferous crowd and the away tie will be key."
Former champions Bayern Munich will start their campaign with a tie against Portugal's Belenenses.
Bayern, who won the competition once in 1996, missed out on a Champions League spot after finishing fourth in the Bundesliga last season.
The ties will be played on 20 September and 4 October
The 40 teams that progress from the first round go into a group phase comprising eight groups of five clubs.
Each team will play two home and two away ties, with the top three teams progressing through to the round of 32, at which point they are joined by eight sides finishing third in their Champions League group.
The final takes place at the City of Manchester Stadium on 14 May.