With his touch, movement, vision and awareness, Modric leaves everyone yearning for more.
Those players who can seduce their audience into watching the individual rather than the team are few and far between.
Just when it appeared that the Croatian midfielder – now aged 35 – was a fading presence after an uninspiring Euro 2020 opening performance against England, he announced himself in this tournament on Tuesday night in the defining group game against Scotland, with a man-of-the-match role topped by a phenomenal goal.
“It looks easy. It looks like he’s 27 or 28, it’s unbelievable,” said his team-mate Dejan Lovren. “He has so much passion in himself, still. It’s a pleasure to play with him.”
“No-one knows how Luka Modric does it,” added head coach, Zlatko Dalic. “Whatever I say about Luka and his game wouldn’t be enough. I am very proud to have such a player and such a captain in my team.”
This week began with the United Nations’ World Refugee Day, celebrating the strength and courage of people who have been forced to flee their home country to escape conflict or persecution.
So, it was perhaps right that football’s most famous refugee made such a mark two days later, at Hampden Park.
Modric was only six years old when, after the break-up of Yugoslavia, the horrors of the Croatian war of independence arrived in his small village of Modrici in December 1991.
Local Serbs supported by the Yugoslav army captured the surrounding area.
Modric’s grandfather, Luka, was killed just a few hundred yards from their home.
The rest of the family fled to a refugee camp in Makarska before finding accommodation in a hotel converted for refugees in Zadar for the remainder of the conflict, while his father went off to war.
Only the player himself knows how life was shaped by those childhood experiences, but before Croatia’s first ever World Cup final, against France, in 2018 he said: “The most important thing is to never give up, never give in to circumstances, believe yourself and to soldier on no matter what’s in your way. Fight for your dreams and success. This is what has always guided me.”
In that same year Modric won the Ballon d’Or. He remains the only player to win it since 2008 who isn’t Messi or Ronaldo.
The award came on the back of his fourth Champions’ League win in five seasons with Real Madrid.
In a team full of galacticos Modric has not always been the main man, but for his country he remains the absolute talisman.
Part of the Croatian side that beat England 3-2 at Wembley in a European Championship qualifier in 2007, he went on to become his country’s youngest scorer in the tournament the following year.
Tuesday night’s goal against Scotland also makes him Croatia’s oldest scorer at the Euros.
Modric’s display in the 2018 World Cup semi-final, where England’s midfield barely laid a glove on him, was one of the principal reasons Croatia progressed to the final.
Were it not for a highly-contentious penalty for France, awarded on a VAR review, there might have been a winners’ medal at the end of that tournament.
The postponement of Euro 2020 by a year did Modric no favours.
He turns 36 in September, but his desire to take Croatia as far as possible is undiminished.
There is a courage to the way Modric plays the game.
His willingness to receive the ball in any position on the pitch, no matter how tight the situation, takes so much pressure away from his team-mates. In possession he allows his team to recover their shape, with opponents frustrated that there will be no opportunity to win the ball back from a misplaced pass or a heavy touch.
And all the time there is the possibility of that killer pass, breaking the lines, turning the opposition around.
Some players visibly lose their effectiveness as they get older but Modric still moves serenely across the pitch, head held high in total control of his surroundings.
In that regard there are similarities with Portugal’s Joao Moutinho, a year younger and with a similarly astonishing number of caps (Moutinho has 134 to Modric’s 141).
Asking him to maintain the performance levels he showed on Tuesday night now that the tournament has moved into the knockout stages may be difficult.
Spain will provide a more arduous test than Scotland, with space much harder to find in a midfield stationed by Rodri, Pedri and Koke. But these are the moments Modric relishes. When the pressure is ramped up he invariably responds.
At the 2018 World Cup, his team-mate Ivan Rakitic hailed Modric as from a ‘different planet who has come to play football with us mortals here’.
It is a fitting description. There are times when Modric is playing a different game to everyone else on the pitch.
If he can muster a handful more of those performances there could still be another chapter in an incredible international career and life story.