They've only won the Estonian top flight twice, but...
Kalju have won the Meistriliiga just twice in their history, with both wins coming within the last ten years. Founded in 1922 as part of the Kalju Sports Club by professional wrestlers Mart Liiv and Aleksander Sneider, the team was effectively wound up at the outbreak of World War II.
Former national team boss Uni Piir, local politician Varner Lootsmann and Anton Siht, president of a local youth team re-established the club in 1997, with the team competing in the fifth their of Estonian football.
Under Piir's leadership, until 2004, Kalju worked their way up through the divisions, eventually winning promotion to the Meistriliiga in 2007 via the play-offs.
Kalju won the league in 2012, with manager (and former player) Igor Prins masterminding a campaign in which they lost just twice, scored 106 goals and conceded just 17. Their results included a 9-0 win away to Kuressaare, a 9-1 drubbing of Viljandi and a 7-0 home win against Tallinna Kalev.
In 2018, Kalju topped the league winning 25 of 36 games, drawing 11 and losing none, finishing two points ahead of Levadia Tallinn and three points clear of Flora Tallinn. Brazilian forward Liliu netted 31 goals over the season.
They're nicknamed the Pink Panthers
The team, originally founded in 1922, traditionally play in black and white.
But in 2007, pink was added to the club's official colours and the team - who play in an all-pink away kit - adopted the nickname.
There's also a team made up of Nomme Kalju fans called JK Roosad Pantrid (Pink Panthers FC) who compete in local leagues.
They've got extensive European experience
Despite their relatively recent return to professional football, Kalju have competed in Europe every season since the 2009/10 campaign.
Memorable results include a 2-1 victory over HJK Helsinki in the 2013/14 UEFA Champions League second qualifying round (although the Estonians lost 10-2 on aggregate to Viktoria Plzen in the following round); a 1-0 win over Lech Poznan in the 2014/15 UEFA Europa League qualifiers; a penalty shoot-out win over Maccabi Haifa in the 2016/17 UEFA Europa League second qualifying round and their last-gasp win over Shkendija in the first qualifying round of this year's Champions League competition.
Aside from the heavy defeat to Plzen, Kalju were also on the wrong end of 5-1 aggregate results against Dnipro and Vaduz.
Who are their key players?
Brazilian forward Liliu, or Ellinton Antonio Costa Morais to give him his birth name, has scored 60 goals in 78 games for Kalju since his arrival on a free transfer from Maltese side Gzira.
Captain Maximiliano Ugge was on Inter Milan's books as a youngster and has experience of playing in Italy, Lithuania and Estonia, and was capped twice for Italy at Under-20 level. He netted the opener against Shkendija.
A couple of Kalju's players have experience of the Scottish game - Mikk Reintam played 12 times for Alloa during the 2015/16 season, while Sander Puri was on St Mirren's books in 2013 and has 77 caps for Estonia.
Who's in charge?
Ukraine national Roman Kozhukhovskyi took the reins in April 2019, ahead of the current campaign. He has previous management experience in Estonia, having been in charge at Johvi Lokomotiv and JK Jarve before spells as assistant boss at Chornomorets Odessa and Karpaty Lviv in his homeland. He joined Kalju initially as assistant boss in December 2018 and took charge of the club's Under-21 side before being appointed the main man.
Where do they play?
Home for Kalju is the intimate Hiiu Stadium but there's a good chance the Estonian leg will be played at the Kadrioru Staadion, where they faced Shkendija and where Scotland famously played for three seconds against nobody in 1996 when Estonia didn't show up. Its usual tenants are Levadia Tallinn, but they tend to play home games at the A. Le Coq Arena so the ground could be free to host the visit of Celtic,.