The former Everton, Celtic, and Real Madrid midfielder was like a grenade in the dressing room everywhere he went, and his life after football makes him a weirdly enigmatic figure now.
Let's start with the nuts and bolts of it. Nuts being the key word - Gravesen just wasn't like any other player.
First of all, throw everything out of the window you thought you knew. The Dane was better than you remember, just sometimes unwilling to follow precise tactical instructions, particularly at Celtic.
Just watch back his highlights against Barcelona in April, 2005, at the Bernabeu - a 4-2 win for Los Blancos and he's in front of the back-four in a midfield diamond.
Gravesen has some rash moments, some awkward and slightly ungainly movements, but these are going to show up when you share the pitch with Zinedine Zidane, David Beckham, Raul and Ronaldo, and are playing opposite Xavi and Andres Iniesta.
He robs Ronaldinho of the ball on several occasions, bullies a young Iniesta off the ball, makes outside of the boot passes and sweeping switches, while also combining expertly with Zidane in some tight situations. Not bad at all.
But that air of bull in a china shop really did earn him a reputation.
In a Madrid derby in March 2006, Gravesen put in another solid display, but a wild-eyed row with Fernando Torres flared up after an off-the-ball barge, while Pablo Ibanez attempted to exact revenge by punching him in the chest at a corner.
He fought with Robinho in one training session and teammate Julio Baptista told Cadena SER: "It was funny. Imagine Gravesen, who was a bit crazy, running at Robinho and grumbling angrily.
"He gave him a kick, then another one. Robinho stopped, looked at him and shoved him in the chest, and then it kicked off. Gravesen wanted to kill him.
"They were separated but Robinho went back to the changing rooms and Gravesen looked and me and said, 'I'm going to kill him.'"
In another training session he had a wrestle with Ronaldo and accidentally knocked out one of his teeth.
Oh, and on his Real Madrid debut against Real Zaragoza, none other than Pele was in attendance, and kicked off the match.
Fighting would see his paths cross with another sporting maverick - Mike Tyson.
In a World Cup qualifier against Iceland in 2001, Gravesen had one of his best ever games, scoring twice. One a deft chip, the other a rasping long range effort in a 6-0 win, and the boxing legend was in the stands.
In Denmark to face Brian Nielsen, Tyson was enamoured with the midfielder, who also got into a scrap or two, and asked for his shirt before wearing it to his weigh-in, and throughout his time in the country.
"I don't know if he still has it - I hope he has, or else," he joked to FourFourTwo.
Now, what were we saying about a grenade in the dressing room? Well, maybe we should say a firework.
Former teammate James McFadden described him as 'hyper' and a 'nightmare' in group scenarios, once bringing a paintball gun into training and shooting people.
"He brought fireworks in one day," the ex-Scotland international told Open Goal. "The physio guy was the fittest guy at the whole club. He was 50, used to play, but if you were injured he would do the running with you, so when you ran he rested and when he ran you rested… So he was out running and Tommy's got this big rocket and shot him, shot the rocket at him."
That wasn't the only incident with fireworks either with David Moyes revealing Gravesen and Everton prodigy Wayne Rooney faced off with each other.
He told Open Goal: "They were in the gym, it at Bellefield it was maybe at that time 60 yards long and I think it was him and Wayne and they were holding the fireworks at one end of the gym to each other and they were shooting the fireworks.
"Actually we had a guy who used to come in, in Liverpool as you can imagine, who would sell us anything and he had big rockets, thick and long, a lot of gunpowder and, you know, they were holding one end and shooting them at each other.
"I'm the manager, I'm the one who is supposed to be saying 'stop that, will you!' But they had already done it."
Even though he had his wild side, he was a good guy, and lovable but at Real, manager Fabio Capello branded him 'peculiar', a claim which McFadden and others can easily stand up.
It's said he didn't have any bills apart from his phone and was always keen on saving money, while Alan Stubbs revealed he would swap between a Nissan Micra and a Porsche Turbo when coming into training.
Summer holidays were spent in his mother's basement playing video games, according to Celtic teammates.
Former Everton captain David Weir recalls Gravesen even found it hard to leave the club for Real, when he joined them in a £2.5million move in January 2005.
"Real Madrid had signed him," he recalled. "Tommy is in the canteen and he did not want to go. Real Madrid had sent this private jet… and you could tell he just did not want to go."
While at the end of his career at Celtic, during an Old Firm derby, Gravesen spent the first half asking Rangers ace Barry Ferguson if he knew any good restaurants in Glasgow.
Prior to returning to Denmark in recent years, Gravesen, after retiring in 2009 aged 32, was to be found living out his days in Las Vegas, reportedly playing poker with vast sums of money.
Rumours swirled about how he got there, to an exclusive part of town where Nicolas Cage and Andre Agassi were his neighbours - but he's kept his cards close to his chest about that.
His reason for return to his homeland to work as a pundit? "I missed football," he said.
Asked if he was as mad as people thought, Gravesen told Sky Sports: "No, not a chance. I wasn't. I just loved it so much and the passion I have for football, it shined through and that, for me, is one of the main things for me. I was just a happy lad."
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