Everton have been drawn in the same Europa League group as Benfica after seeing off Sigma Olomouc while Fulham have two mouthwatering matches against AS Roma to look forward to.
David Moyes' side also face games against AEK Athens and BATE Borisov, but it will be the matches against the 31-times Portuguese League winners that will be most eagerly awaited.
Benfica only finished third in their league last year as did AEK after the Greek League play-offs.
Belarussian side Borisov qualified for the group stages of the Champions League last term and are the reigning domestic league champions.
As well as facing Francesco Totti and co, Fulham also have tough encounters with Basel and CSKA Sofia to contend with.
Basel were third in last season's Swiss Super League while CSKA, 31-times winners of the Bulgarian League, finished second last term.
Celtic, knocked out of the Champions League by Arsenal, have been paired with last season's UEFA Cup semi-finalists Hamburg, Hapoel Tel Aviv and Rapid Vienna.
Elsewhere, last season's winners of the UEFA Cup, Shakhtar Donetsk, are in the same group as Club Brugge, Partizan Belgrade and Toulouse.