Here, Press Association Sport looks at some of the talking points following the draw for the first knockout round, to be played in February.
Gunners having an early night
With Arsenal and Chelsea both seeded for the first knockout round, UEFA announced ahead of the draw that Arsenal's second-leg tie would take place a day earlier, due to regulations stating the pair cannot play in the same city on the same night. UEFA also said the kick-off time would be 5pm, to avoid a clash with Champions League fixtures. European football's governing body reneged on that after fan unrest, pushing kick-off back 24 hours and 55 minutes. The Gunners, who wanted an 8pm start, said: "We appreciate this kick-off time may present difficulties for our supporters."
Familiar opposition for Arsenal
Arsenal played BATE Borisov in the Europa League group stage in 2017-18, winning 4-2 in Belarus and 6-0 at home. Former Arsenal midfielder Aleksandr Hleb is now in the BATE squad, at the age of 37, and played against Chelsea in the group stage this season. The Blues beat BATE 3-1 at home and 1-0 in Belarus. Celtic's opponents Valencia have former Arsenal players Gabriel Paulista and Francis Coquelin in their ranks, plus on-loan Chelsea striker Michy Batshuayi.
Bhoys braced for Valencia
Celtic suffered for finishing second in Group B, behind Red Bull Salzburg, by being drawn with Valencia. Like Celtic in earlier rounds, Valencia parachuted into the competition from the Champions League but the Spaniards may not be the force they once were. They are a lowly 14th in LaLiga and finished behind Juventus and Manchester United in their Champions League group. However, they did beat United at the Mestalla, although both sides' fate was already sealed.
Malmo are a familiar name in continental competition and reached the European Cup final in 1979, losing to Brian Clough's Nottingham Forest. Their former players include Zlatan Ibrahimovic and one former manager is Roy Hodgson, now at Crystal Palace. The current boss is former Manchester City striker Uwe Rosler. Rosler has managed four English teams, the first of them Brentford, whose Griffin Park home is just six miles from Chelsea's Stamford Bridge. Rosler's Brentford took Chelsea to an FA Cup fourth-round replay in 2013.
It might have been tougher
There are 10 former winners in the last 32, including Chelsea. Some big sides have been drawn against each other. Five-time champions Sevilla play Lazio and former winners Shakhtar Donetsk and Eintracht Frankfurt meet each other, while Benfica and Galatasaray have been drawn in opposition.