On Tuesday, they face Bournemouth in the fourth round of the competition - only the third time they have reached that stage in their history. And they got their by beating Premier League Leeds United at home 3-0.
See our graphic below which shows 13 of the top giant-killings in FA Cup history and the amount of league places between the sides involved
And on both occasions, against Torquay United and Hull City, they won and set up ties against Premier League opposition - Manchester United (2010/11) and Stoke City (2011/12).
The cup is famed for its giant kills, and BetVictor have crunched the numbers to unveil exactly who is the biggest giant killer of all time. How do Crawley Town's wins against Hull City, Derby County and Leeds compare to other giant-killings?
According to the data, the Giant Killers of the FA Cup found that Luton have performed the biggest individual upset over the years, overcoming a gap of 88 league positions. Chorley's win over Derby saw the club overcome 83 positions, behind only Luton and Shrewsbury's famous win over Everton (85 places). However, a win over Wolves on Friday would see the non-league side overcome 111 league places and become the biggest giant killer of the past two and a half decades.
Overall, Oldham are the biggest giant killers in the competition over the past 25 years, having defeated teams a cumulative 264 places above them down the years. Sheffield United are the biggest giant killers still left in the competition according to the data, although they are in the position of giants this weekend as they take on Plymouth, a side 35 places below them in the football pyramid.
Crawley, are currently the fifth biggest giant killer in the competition but could become the second largest giant killer with a win over Bournemouth at the weekend, while Doncaster may look to shock West Ham, with the Hammers having lost to teams a cumulative 310 places below them, the highest of any team until both Leeds' and Derby's defeats a fortnight ago.
You can view the full details on BetVictor's website here