They now potentially stand just 90 minutes away from their first major tournament final in 52 years, when they last won the World Cup back in 1966.
They have endured the emotional tugs of two penalty shootouts, somehow coming out on top on both occasions, the first team since 1990 to do so at a World Cup.
"Clearly, we wanted to go even further but sadly today we could not", coach Stanislav Cherchesov said, addressing the crowd.
She said that after Croatia joined the EU in 2013, 'I wish we start living the lives of people in the European Union'. Both of these countries have needed luck on their side to get to this point, with England needing penalties to get past Colombia, and Croatia prevailing twice in shootouts - against Denmark and Russian Federation.
It is only the second time that Croatia have reached the World Cup semi-finals.
The Croatians looked more comfortable from the spot, netting four of their five attempts with midfielder Ivan Rakitic firing home the decisive effort to put them into the semi-finals, prompting tears from Croatia coach Zlatko Dalic.
They will face England, who beat Sweden 2-0 earlier, at the Luzhniki Stadium Moscow on Wednesday.
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Croatia earned their shot at England after beating hosts Russian Federation 4-3 on penalties after the match was tied 2-2 after extra-time as Denis Cheryshev and Mario Fernandes traded goals with Andrej Kramaric and Domagoj Vida.
"We've been always returning to the 1998 team, putting a new burden on Modric and his team".
Meanwhile, Dele Alli, who scored England's second goal, said it was a great team performance.
Goals out of 20 that Russian Federation conceded at the World Cup as an independent nation have been from set pieces.
"This makes us extremely proud that after 20 years we've reached the semis of the World Cup", the 32-year-old Modric added.
Subasic's four shootout saves are tied with Harald Schumacher of West Germany and Sergio Goygochea of Argentina for the most in a single World Cup. It will be a battle again but I believe in us.