Both countries needed penalties to reach the semi-finals, with Croatia eliminating tournament favourites Brazil and La Albiceleste overcoming Netherlands.
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One more victory for both would put them within one game of redemption as Argentina were beaten finalists in 2014.
Croatia are bidding to reach a second successive final where they could even face a rematch with defending champions France if they're victorious against Morocco.
Croatia v Argentina: How to watch on TV
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This semi-final tie will kick-off at 7pm UK time (10pm local time) on Tuesday, December 13.
It is being shown on ITV One from 6:15pm.
It will be shown free-to-air and you can also live stream it for free on the ITVX.
Croatia v Argentina: How to listen on the radio
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Adrian Durham will be your host with Jim Proudfoot and Stuart Pearce providing commentary.
talkSPORT.com will also have a live blog of the action too.
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Croatia v Argentina: Squads and team news
Croatia have a full bill of health to contend with after Borna Sosa and Mislav Orsic both recovered from illness.
Albiceleste full-backs Gonzalo Montiel and Marcos Acuna are both suspended after they picked up bookings last time out.
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Croatia
Goalkeepers : Dominik Livakovic, Ivica Ivusic, Ivo Grbic
Defenders : Domagoj Vida, Dejan Lovren, Borna Barisic, Josip Juranovic, Josko Gvardiol, Borna Sosa, Josip Stanisic, Martin Erlic, Josip Šutalo
Midfielders : Luka Modric, Mateo Kovacic, Marcelo Brozovic, Mario Pasalić, Nikola Vlasic, Lovro Majer, Kristijan Jakic, Luka Sucic
Forwards : Ivan Perisic, Andrej Kramaric, Bruno Petkovic, Mislav Orsic, Ante Budimir, Marko Livaja
Argentina
Goalkeepers: Emiliano Martinez, Geronimo Rulli, Franco Armani
Defenders: Nahuel Molina, Gonzalo Montiel, Cristian Romero, German Pezzella, Nicolas Otamendi, Lisandro Martinez, Marcos Acuna, Nicolas Tagliafico, Juan Foyth
Midfielders: Rodrigo De Paul, Leandro Paredes, Alexis Mac Allister, Guido Rodriguez, Alejandro Gomez, Enzo Fernandez, Exequiel Palacios
Forwards: Angel di Maria, Lautaro Martinez, Julian Alvarez, Nicolas Gonzalez, Joaquin Correa, Paulo Dybala, Lionel Messi
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Croatia v Argentina: Match facts
Luka Modric has made the most World Cup appearances (17) and most appearances at major tournaments (30) for Croatia. He's started all five of their 2022 World Cup matches and could become only the fourth player to start six matches at a World Cup aged 37+, after Brazil's Nilton Santos in 1962, Italy's Dino Zoff in 1982 and England's Peter Shilton in 1990.
Argentina's Lionel Messi has both scored and assisted a goal in three different World Cup matches, including two at this year's tournament (vs Mexico and Netherlands). Since 1966, no player has ever done so in four separate games.
If Lionel Messi plays, he will equal Lothar Matthäus for the most appearances in World Cup history (25). As well as being Argentina's joint-highest goalscorer in the competition (10), he's one assist away from equalling Diego Maradona's overall record of eight at World Cup finals (since 1966).
Croatia have won all four of their penalty shootouts at the World Cup, knocking out Japan and Brazil in the last 16 and quarter-final in 2022 respectively. The only nation to win more penalty shootouts in the competition are Argentina (5).
Argentina have scored first in all five World Cup matches this year, although they failed to win after going two goals ahead in a World Cup match for the first time in their 2-2 draw with the Netherlands. Indeed, 12 of the last 13 goals they've conceded at the World Cup have come in the second half of matches.
Croatia have never failed to score in their 10 World Cup knockout stage matches. However, they've also conceded at least once in each of their last eight, with five of their last six such games going to extra time.
Despite being on the verge of reaching consecutive finals, Croatia haven't scored first in any of their last nine World Cup games, since a 2-1 win over Iceland in the 2018 group stages. This is the furthest into the competition any side has got without opening the scoring in any of their matches.
Argentina have won just one of their last seven World Cup games against European sides (D3 L3), beating Poland 2-0 in the group stages this year. However, two of those three draws have resulted in penalty shootout victories.
Following their penalty shootout victory against Brazil in the quarter-final, Croatia could become just the second side to eliminate both Brazil and Argentina from the knockout stages of the same World Cup, after Germany in 2014.
Croatia were losing finalists in 2018, and could become the fourth European nation to reach consecutive World Cup finals after Italy (1934, 1938), Netherlands (1974, 1978) and Germany (1982, 1986, 1990).
Argentina are looking to reach the World Cup final for the sixth time, a figure bettered only by Germany (8). They've never been eliminated at the semi-final stage before, most recently beating the Netherlands in 2014.
This is the third World Cup meeting between Argentina and Croatia, and first in the knockout stages. Argentina won 1-0 in 1998, before Croatia's 3-0 win in the 2018 edition in Russia.