Manchester United were handed a tricky Europa League last 16 tie against Real Sociedad while Tottenham Hotspur will play Dutch side AZ Alkmaar after the draw was held on Friday, but both managers are more concerned about their Premier League form.
Holders Sevilla swept into a second consecutive Europa League final.
Jonatan Soriano's love affair with the Europa League continued as last season's top scorer grabbed a hat-trick on Thursday to help Salzburg become one of four teams to reach the knockout stages.
Manchester United, Sevilla and Celtic led a parade of clubs with continental pedigree to book the first places in this season's Europa League knockout stage.
Fellow Serie A sides Atalanta and Lazio also won while Portugal's Vitoria Guimaraes began their match against Salzburg with not a single European player in the team.
Jonathan Soriano scored an incredible goal from near the halfway line to complete a stunning 3-0 win for Salzburg away to once-mighty Ajax Amsterdam in the Europa League round of 32 on Thursday.
Napoli began their Europa League group stage campaign in scintillating fashion.
Villarreal's Adrian Lopez produced a stinging sucker punch in stoppage time to leave Liverpool reeling and move the Spaniards closer to a maiden European final after their Europa League last four first leg clash finished 1-0 on Thursday.
IMAGES from Europa League matches played on Thursday.
Former European champions Ajax Amsterdam and Celtic, who both suffered the indignity of being knocked of the Champions League qualifiers by underdogs this season, will meet in the Europa Leagueafter being drawn together in the group stage on Friday.
Kazakhstan's Astana fought back to beat a youthful Manchester United side 2-1 at home, Arsenal's woes continued as Frankfurt's Daichi Kamada scored twice to secure a 2-1 win.
Chelsea beat Eintracht Frankfurt on penalties on Thursday to set up an all-English Europa League final with local rivals Arsenal in Baku on May 29.
Burnley reached the Europa League third qualifying round with a 3-1 win over Aberdeen after extra time at Turf Moor on Thursday but now face another tough battle to increase their squad size.
Carlos Bacca claimed the plaudits with a superb double strike, including a late winner to decide a pulsating clash that began at a hair-raising pace with four goals in the first half.
London sides Tottenham Hotspur and Arsenal made winning starts as did fellow Premier League club Leicester City.
Scotland defeated Haiti 1-0 in a World Cup Group C match, with John McGinn scoring the winning goal. This victory marks Scotland's first win in the tournament since 1990, placing them at the top of their group. Haiti, despite their pace, lacked the finishing touch.
Sevilla coach Unai Emery has been picking the brains of Juande Ramos as he tries to plot the downfall of Ukrainian outsiders Dnipro Dnipropetrovsk in Wednesday's Europa League final.
Napoli kept alive their hopes of advancing from Group C after Lorenzo Insigne, Victor Osimhen and Matteo Politano secured a 3-0 home win over Legia Warsaw.
Arsenal teenager Bukayo Saka scored his first goal for the club as they beat 10-man Eintracht Frankfurt 3-0, while Manchester United's 17-year-old Mason Greenwood secured a 1-0 win over FC Astana as the Europa League group stage began on Thursday.
Arsenal and Chelsea were among seven teams to reach the Europa League knockout stage on Thursday, while last year's runners-up Olympique de Marseille were eliminated at the group phase.
Four-time European Champions Ajax Amsterdam were felled at the first hurdle of the continent's second tier Europa League on Thursday, exiting in the group stage two days after rivals PSV Eindhoven celebrated long-awaited success.
Yet Milan's defensive frailty was punished when Konstantinos Fortounis scored from the penalty spot in the 81st minute to give his side the win that left them second in Group F on 10 points.
Rashford scores a brace as Man United fight back to beat Omonia
Red Star, who won the European Cup in 1991 and reached the latter stages the following season, finished second in Group H behind Arsenal who crushed BATE Borisov 6-0.
New Liverpool boss Juergen Klopp made it three wins from his last three matches with a 1-0 success at Rubin Kazan in Russia that left them second in Group B, two points behind Swiss club Sion on Thursday.
Thirteen teams have now qualified for the last 32 including Bayer Leverkusen, FC Zurich and Lazio who had already secured places in the next stage of the competition.
Manchester United's Paul Pogba and Henrikh Mkhitaryan scored a goal in each half as their team comfortably outclassed Ajax Amsterdam to win an emotional Europa League final 2-0 and qualify for the group stages of the Champions League.
The decision followed talks with Greek authorities, UEFA said.
The value of an in-form striker was underlined as Tottenham Hotspur, Liverpool and Athletic Bilbao needed goals from pivotal front men to grab vital wins that booked places in the Europa League last 32 on Thursday.
Goals from Jan Vertonghen and Jermain Defoe left Tottenham Hotspur on the cusp of the Europa League knockout stages as four other clubs maintained perfect starts on Thursday.
Xabi Alonso will take over as Chelsea's new manager, the Premier League club said on Sunday, with the Spaniard signing a four-year deal beginning on July 1.
IMAGES from the Europa League matches played on Thursday
United climbed to fourth in the standings on 15 points going into the last round of matches, in a strong position to reach the knockout phase along with Spurs who are sixth with 14 points.
Real Madrid will play local rivals Atletico Madrid while Bayern Munich were drawn against Bundesliga title challengers Bayer Leverkusen on Friday.
News of all that's transpired on and off the football field
If two or more clubs are level on points at the end of the group stage, a number of criteria will be taken into consideration to decide the qualifiers for the next round, starting with the head-to-head record among the teams in question. It then goes to superior goal difference and then goals scored in those matches.
IMAGES from Europa League matches played on Thursday.
Cristiano Ronaldo scored on his return to the starting line-up as Manchester United sealed a place in the Europa League knock-out rounds with a 3-0 victory over Sheriff Tiraspol at Old Trafford on Thursday.
A round-up of Tuesday's action in the UEFA Champions League.
Images from action in the Europa League matches on Thursday.
