Germany not to qualify at 6/1 (betway)
France/Portugal dual forecast at 4/1 (betway)
Odds - Title: 500/1; To win group: 40/1; To qualify: 5/1
Best European Championship performance: Third (1964)
How they qualified
Via play-offs (Fourth, Group E - P8 W4 D0 L4 F8 A11 Pts12)
Qualified in dramatic style, scoring in the 88th and 92nd minutes of their play-off final with Iceland to post a 2-1 win and reach the Finals.
They had previously seen off Bulgaria as they came through what was technically the toughest of the four play-off 'paths'.
Despite problems scoring goals (just eight in eight games), Hungary had narrowly missed out on automatic qualification. They went into their final group match needing to beat Wales to secure a top-two finish but ended up two points behind the Welsh following a 2-0 loss in Cardiff.
World Cup qualifying started well enough with seven points from nine claimed, although they will be perhaps slightly disappointed not to have beaten Poland, likely rivals for second spot. They had led 2-0 but conceded a late equaliser to draw 3-3 in Budapest.
Dominik Szoboszlai is undoubtedly Hungary's brightest star. Sadly for the Magyars, the man who scored their late play-off final winner has been ruled out of the tournament due to injury.
Having made his name at Salzburg, the midfielder joined Red Bull Leipzig in January but is yet to make his debut for the Bundesliga club due to a thigh problem. His absence is a massive blow in terms of creativity, particularly given Hungary's tough draw.
Two of Szoboszlai's Leipzig team-mates will be key members of the squad though.
Keeper Peter Gulacsi is a safe pair of hands, while in front of him Willi Orban marshals the defence.
Bristol City's Adam Nagy looks likely to play a major role in stopping opponents in his defensive-midfield role but goals are likely to be a problem with much resting on 33-year-old Adam Szalai, who struggled at Mainz this season.
Marco Rossi - Appointed to his current role in 2018 having caught the eye of the national federation by leading Honved to the Hungarian title in 2016/17.
The Italian enjoyed a lengthy playing career in Serie A, one which also took him to Club America in Mexico. There he worked under current Leeds boss Marcelo Bielsa and says he has learned a lot from the Argentine in terms of how he manages his teams.
Odds - Title: 10/1; To win group: 7/2; To qualify: 1/3
Best European Championship performance: Winners (2016)
How they qualified
Second, Group B - P8 W5 D2 L1 F22 A6 Pts17
The reigning European champions could only finish runners-up in their group to Ukraine, drawing at home to them and losing 2-1 away.
Qualification was eventually secured in the final game, a late Cristiano Ronaldo goal sealing a 2-0 victory in Luxembourg.
One title Portugal definitely won't be retaining in 2021 is the Nations League crown. A home defeat to France in November proved costly as they could only finish second behind the world champions.
They posted early World Cup qualifying wins over Ireland and Luxembourg but were held 2-2 in Serbia despite taking a 2-0 lead.
This Portugal squad looks better than the one which won the European title five years ago.
It would be easy to suggest Cristiano Ronaldo is past his best at 36 but the fact is he scored 11 goals in qualifying (only Harry Kane netted more) and has just finished as top scorer in Serie A.
There are plenty of other forward options too, a fact which has led boss Fernando Santos to test out a more expansive 4-3-3 formation in recent times.
Only Robert Lewandowski scored more in the Bundesliga this season than Andre Silva, Bernardo Silva is a Premier League winner (again), Joao Felix has just won La Liga with Atletico Madrid and Diogo Jota comes in off a strong debut season at Liverpool.
In midfield, Danilo Pereira's star is rising with William Carvalho and Joao Moutinho other options.
Manchester City's Ruben Dias, who could be named PFA Player of the Year on Sunday, will control a defence also likely to feature Jose Fonte, once of Southampton, now a Ligue 1 winner with Lille. Fonte is set to keep fellow veteran Pepe out of the starting XI, which is also likely to feature Dias' clubmate Joao Cancelo.
Fernando Santos - Hugely-experienced manager who earned legendary status by guiding Portugal to Euro 2016 glory.
Has been in this job since 2014, prior to which he managed Greece at Euro 2012 and the 2014 World Cup. That appointment followed spells at the top Greek clubs, while his career in club soccer has also seen him manage Portugal's 'Big Three' - Porto, Benfica and Sporting Lisbon.
Despite the 2016 win, Santos had his critics for the style of Portugal's play and there's an argument to be made that he is still not getting the most out of a very talented squad of players.
Odds - Title: 5/1; To win group: 17/10; To qualify: 1/8
Best European Championship performance: Winners (1984, 2000)
How they qualified
First, Group H - P10 W8 D1 L1 F25 A6 Pts25
The world champions finished top of their group despite taking just one point from their two games with runners-up Turkey.
They subsequently needed to win in Albania in their final game to book their Finals berth but did so with a 2-0 victory.
Certainly weren't as convincing in qualifying as some of their fellow title contenders.
Edged out Portugal to win their Nations League group back in the autumn, winning five and drawing one of their six games.
Kicked off World Cup qualifying with a disappointing 1-1 draw at home to Ukraine to continue the feeling that Les Bleus are not performing at the level which took them to World Cup glory three years ago.
However, they have lost just three times in 29 games since Russia 2018.
The French squad is frankly an embarrassment of riches.
It still features the majority of the 2018 World Cup winners but is arguably growing stronger all the time.
Still, it is in forward areas where the depth of talent is arguably at its greatest.
Kylian Mbappe won the World Cup as a teenager and has continued his upward trajectory since. The lightning-fast forward has the potential to light up this tournament.
Antoine Griezmann, top scorer at Euro 2016, also remains with the only question being whether Didier Deschamps will continue to put his trust in Chelsea's Oliier Gviroud, who has started and scored regularly from his country during his time, largely on the bench, at Stamford Bridge.
He top-scored for Les Bleus in qualifying but his position is coming under threat, especially given the inclusion of Real Madrid's Karim Benzema after years in the international wilderness.
I've not even mentioned Hugo Lloris, Benjamin Pavard, Kingsley Coman, Ousmane Dembele, Adrien Rabiot or, if you want to feel old, Marcus Thuram - son of 1998 World Cup winner, Lilian.
Essentially the talent is there and anything short of victory will be deemed a failure in France. The pressure is firmly on the bookies' favourites.
Didier Deschamps - One of only three men to have won the World Cup as both a player and manager. Came close to the same European Championship double but France lost in the Euro 2016 final.
Has spent almost a decade in the job having replaced Laurent Blanc back in 2012. Has had his critics in that time and expectation remains sky high given the players at his disposal.
Has recently tried out different tactical formations to enhance the feeling that France are not quite the finished article heading into this tournament.
Odds - Title: 9/1; To win group: 33/20; To qualify: 1/8
Best European Championship performance: Winners (1972, 1980, 1996 - first two as West Germany)
How they qualified
First, Group C - P8 W7 D0 L1 F30 A7 Pts21
Managed to top their group despite losing at home to the Netherlands, a last-minute winner in the reverse fixture proving crucial to the final standings.
Scored 20 goals in their four home games, noteworthy given they will be on home soil for their three group games.
Frankly poor. The Germans won only two of their six Nations League games and were thrashed 6-0 by Spain, who won the group to deny Die Mannschaft a place in the Finals. It was their heaviest defeat since 1931.
They are hardly heading into the Euros full of confidence.
Thomas Muller and Mats Hummels' form for Bayern Munich - coupled with some iffy performances from the German side - have seen the veteran pair return to the fold in what is frankly a bit of a U-turn by the manager.
Whether either can force his way into the starting XI remains to be seen but their presence certainly makes the squad stronger.
There's an argument Hummels could join Chelsea's Antonio Rudiger in central defence but despite having the highest number of assists in the top European leagues this season, Muller may be struggling for a starting spot given his rivals in that position - think Toni Kroos and Leon Goretzka.
Joshua Kimmich, another Bayern star, will sit in midfield, although he is able to link the defence and attack, as 14 assists this season show.
Up front, Serge Gnabry has been the focal point of the attack of late, playing as a centre forward rather than in the wider role he performs for Bayern. The former Arsenal man bagged eight goals in qualifying as a result.
Leroy Sane and Timo Werner inject further pace into a forward line which certainly has the potential to trouble any defence.
Defensively perhaps, Germany are not as strong as they once were but in Manuel Neuer they still have a top-class keeper.
Joachim Low - Is one of the longest-serving international managers, having spent almost 15 years in the job. However, Low has already announced this tournament will be his swansong - he is stepping down at its conclusion.
Low's career highlight will forever be leading the Germans to glory at the 2014 World Cup in Brazil where they crushed the hosts 7-1 in the semis before edging out Argentina 1-0 in the final.
Four years later came the lowlight with Germany bounced out of the World Cup in the group stage for the very first time.
Low will hope for one final flourish from his side - and a first European title for himself - but recent form suggests it may be a struggle.
There's no doubting this is Euro 2020's 'Group of Death' given it features three of the top six in the outright betting.
However, given a format which means all three could progress to the last 16, it's not as deadly as it would once have been.
It is the only group not to have an odds-on favourite. France are the market leaders in terms of winning the group with some firms but they will have to play away to both Germany and Hungary.
The Germans will look to make the most of home advantage with all three of their games in Munich but it's hard to be too confident about their chances given recent events which include that 6-0 humbling by Spain and a shock home defeat to North Macedonia.
There's also the U-turn by Joachim Low over Thomas Muller and Mats Hummels which doesn't reflect well on the soon-to-be-gone manager.
In short, I think there's potential for things to unravel for the Germans - just as they did at the last World Cup.
They open against France and then meet Portugal. Are two home defeats really out of the question against such strong opposition? If that were the case, even a win over Hungary in their final game might not be enough to secure progress.
I can't resist the 12/1 dangled by betway about the Germans failing to qualify.
France/Portugal in the dual forecast at 4/1 with the same firm also looks decent given the duo look to have two of the strongest squads in the tournament.
* Odds correct at time of publication