The League Two side's remarkable progress through to the showpiece match at Wembley gives them the opportunity to become the first club in football history - from any European country - to win a national cup competition while playing in the fourth tier.
If the Bantams go on to triumph against Swansea on Sunday, it would make Phil Parkinson's side the first fourth-tier team in world football history to win any national cup (from countries ranked inside Fifa's top 100). This is far from a normal state of affairs.
In having reached the final at all, Bradford have joined just Rochdale in the League Cup final of 1962 and Calais in the 2000 French Cup final to have done so before.
But what are the greatest ever existing cup final upsets? We round up a few of our favourites.
Sunderland beat Leeds 1-0 in the 1973 FA Cup final
Leeds boasted a dominant First Division team with 10 international players and came to the match as the cup holders, for their third final in four years; Sunderland, meanwhile, came from the second tier, where they were third from bottom.
No Second Division side had won the cup for more than 40 years, but midfielder Ian Porterfield's right-footed finish proved the deciding goal, with Sunderland goalkeeper Jimmy Montgomery making a string of memorable match-winning saves.
Steaua Bucharest beat Barcelona on penalties in the 1986 European Cup final
Steaua Bucharest's 1986 European Cup final teamSteaua became the first Eastern European side to win the European Cup in 1986 as they produced a remarkable victory over Spanish giants Barcelona, who enjoyed tremendous support with the match played in Seville.
The Romanian side benefited hugely from the heroics of goalkeeper Helmuth Duckadam, who followed keeping a clean sheet against Terry Venables's much-fancied side, who were the Spanish champions, by saving all four of Barcelona's penalties to win the cup.
Steaua, who had not previously triumphed in any European competition, went on to claim the Super Cup later that year, while they finished as runners-up to AC Milan in the European Cup in 1989.
Greece beat Portugal 1-0 in the Euro 2004 final
Otto Rehhagel's side lost their first two matches in qualification for the tournament, and to Russia in the group stages in Portugal, but shock wins over Spain, reigning champions France, the Czech Republic and then the hosts saw them triumph.
It was by far the country's greatest sporting achievement in a team sport, and saw the players appear on stamps and receive medals from the President of Greece as the team shot up the world rankings, from 35th before the start of the tournament, to 14th.
Uruguay beat Brazil 2-1 in the 1950 World Cup final
Unlike other World Cups, in 1950 the winner was decided by a final group stage, and Brazil only needed to avoid defeat to claim the trophy, but Uruguay managed a thrilling 2-1 victory in Rio de Janeiro.
Brazil took the lead in the second half to make the odds of an amazing upset all the more unlikely, but Uruguay roared back with goals from Juan Alberto Schiaffino and Alcides Ghiggia - who struck with just 11 minutes left in the match - and clinched the win.
The result is considered to be one of the greatest upsets in football history, and the term 'Maracanazo' (loosely translated as 'The Maracana Blow') has become synonymous with the match, with Uruguay lifting the trophy in front of a crowd of 173,850.
Southampton beat Manchester United 1-0 in the 1976 FA Cup final
United came into the match as the overwhelming favourites, having finished third in the First Division that season and against a Southampton side that ended up sixth in the second tier.
The top-division side, managed by Tommy Doherty, squandered numerous chances as Southampton goalkeeper Ian Turner made a collection of breathtaking saves, and the match drifted towards extra-time.
But Southampton had the last word as left winger Bobby Stokes put his name in history as he received Jim McCalliog's pass and beat Alex Stepney to net the winner and secure the Saints' first major trophy.
Aberdeen beat Real Madrid 2-1 in the 1983 Cup Winners' Cup final
Eric Black's opener was cancelled out by Juanito's penalty in normal time, before John Hewitt clinched a historic victory for Fergie's men, who had earlier sealed a notable 3-2 quarter-final win over Bayern Munich in the competition.
Aberdeen became the only Scottish team to win two European trophies, also defeating European Cup holders Hamburg to win the Super Cup. It was also the second and last time that the trophy went to Scotland, following Rangers' victory in 1972.
Zambia beat Ivory Coast on penalties in the 2012 African Cup of Nations final
Zambia's 2012 African Cup of Nations win was remarkable for many reasons, not least because of who they beat to claim their first major title: the star-studded and much fancied Ivory Coast.
While none of Zambia’s players are household names of any sort – Chris Katongo was the biggest star in that squad - they played as a team and not a collection of highly-rated individuals, with an inspired win over Ivory Coast in the final as they frustrated Didier Drogba’s Elephants and nicked a penalty shoot-out win.
Perhaps the most enduring image was of coach Herve Renard carrying injured defender Joseph Musonda on to the pitch to join in his team-mates' celebrations post victory, with the veteran left-back having exited the field in tears after twisting his ankle early in the match. Renard’s gesture inspired tears of a distant kind, and he will always be a hero in the African country.
Coventry City beat Tottenham 3-2 in the 1987 FA Cup final
Spurs were appearing in their third final in seven seasons, having won the trophy in 1981 and 1982, and were huge favourites against a Coventry side that were appearing in their first ever domestic cup final.
In one of the finest cup matches of all-time, Tottenham took the lead in just the second minute of the match through striker Clive Allen, and Coventry had to equalise twice to get back on level terms when they looked dead and buried.
The match went into extra-time, and an own goal from Gary Mabbutt gave Coventry a dramatic victory as Ray Clemence was beaten in the Spurs goal. A Coventry fanzine remains entitled 'Gary Mabbutt's Knee' in tribute to the winner.
Celtic beat Internazionale 2-1 in the 1967 European Cup final
Jock Stein's Celtic became the first Scottish, British and northern European club to win the European Cup in 1967 as the Glasgow side collected the trophy with 11 Scots, all of them born within 30 miles of Celtic Park, when they overcame Inter Milan 2-1 at Lisbon's Estadio Nacional.
"Eleven players of the same nation will never win the Champions League again," commented Tommy Gemmell, scorer of the equalising goal before Steve Chalmers produced the winner in the death throes of the final.
"We had 11 Scots, and that is unbelievable when you think how small a nation we came from. You'll never get that happening again, never mind all being within 20-odd miles of the club's home ground."
Winger Jimmy Johnstone, voted as Celtic's greatest player by the club's fans, said Celtic's European Cup winners were a "speeded up version" of the Dutch's total football philosophy.
QPR beat West Brom 3-2 in the 1967 League Cup final
QPR players celebrate winning the League CupQueens Park Rangers were another of the three sides in English football history to have won a cup from the third tier as they beat West Brom 3-2 in the League Cup final.
The Baggies received a bye through the first round, with QPR having to play an extra game en route to the final, but goals from Roger Morgan, Rodney Marsh and Mark Lazarus secured a famous win to claim the trophy.
Sadly for Rangers, the FA refused to let them compete in the Inter-Cities Fairs Cup, despite the fact that their victory in the final should have given them automatic qualification, with a First Division side taking their place in the European competition.
Tottenham beat Sheffield United 3-1 in the 1901 FA Cup final replay
Spurs were a non-league time back in 1901 - of the third-tier Southern League - and it was a stunning victory for the north London side as they defeated First Division Sheffield United 3-1 in a replay, having drawn 2-2 in the initial final.
Swindon beat Arsenal 3-1 in the 1969 League Cup final
Swindon's Stan Harland with manager Danny WilliamsFirst Division Arsenal were regarded as certain winners of the clash at Wembley, with Swindon a lowly third-tier side and appearing in their first League Cup final.
However, with eight Arsenal players suffering from flu and a terrible boggy pitch due to heavy rain and the Horse of the Year show having been staged at the London venue in the same week, Swindon competed bravely to claim a magnificent win.
A late equaliser from Gunners forward Bobby Gould took the match into extra-time after Roger Smart's opener, but a brace from striker Don Rogers gave Swindon victory. Sadly for Danny Williams's side, they were not eligible for a place in the UEFA Cup as they were not in the First Division.
Wimbledon beat Liverpool 1-0 in the 1988 FA Cup final
It was the classic cup upset from an unfashionable, unfancied side against one of the most dominant teams of the era as Wimbledon beat the newly-crowned First Division champions Liverpool at Wembley.
The result was comfortably one of the biggest shocks in the history of British football as the London side won the cup for the first and only time in their history, with Laurie Sanchez heading the game's only goal in the first half.
The match was also memorable for the first ever penalty save in an FA Cup final as Dave Beasant palmed away John Aldridge's effort to clinch an incredible victory for the Crazy Gang. Wimbledon were not allowed to compete in the Cup Winners' Cup due to the ongoing ban on English teams from European competitions.
It is now time to hear from you: what are your all-time favourite cup final upsets? Post them below!