The match will be their 400th competitive meeting but it is perhaps the most uneven contest between the two Glasgow giants since they first met in 1888.
The clubs have dominated Scottish football, winning 95 of the available Scottish top flight titles since 1890
However, Celtic will enter Sunday's semi-final clash as overwhelming favourites to progress following an amazing fall from grace by Rangers in recent years.
The match at Hampden will be the first meeting of the Old Firm since April 2012 with Rangers subsequently forced to start life again in the country's bottom tier following liquidation in June 2012.
Their absence from the Premiership has allowed Celtic to dominate with the Parkhead club, who top the table by three points, on course for their fourth league title in a row
In contrast Rangers, who have won back-to-back promotions, are trailing Hearts by 13 points in the race for the Scottish Championship title and a place back in the top flight.
The picture off the field looks no better for Rangers, who just seven years ago were competing in the UEFA Cup final
The Ibrox club remain mired in financial uncertainty and this week accepted a £10million crisis loan from Newcastle United owner Mike Ashley's Sports Direct empire.
The loss of the four matches against Rangers a season has carried a cost for Celtic too, with their chief executive Peter Lawwell estimating that their rivals absence was costing the club £10m a year in lost revenue.
Rangers caretaker manager Kenny McDowall, in charge for the match following Ally McCoist's resignation in December, hopes the return of the derby will give a much-needed boost to Scottish football.
"I think Scottish football needs this fixture," McDowall, who is also working his 12-month notice at the club, said.
"Hopefully it will help Scotland get back to better things in the future.
"There's obviously a gap and Celtic are the Scottish champions.
"I don't think there's ever been such a gap as there is at this moment, so that's what makes it a difficult game and that's why the bookies are making them favourites.
"But, as we all know, it's the Cup and cup football can bring surprises
The biggest thing for me is the players put on a performance for themselves and our supporters and do themselves proud.
"If we do well enough to get to the final then I'll be delighted."
The fixture has caused a re-emergence of the controversial debate over whether Rangers are a new club following liquidation three years ago
A section of Celtic fans paid for a full page advert in a Scottish newspaper last weekend, claiming the 'Old Firm' derby was dead.
However, Celtic manager Ronny Deila avoided the controversy.
"It's a first meeting with Rangers for me," the Norwegian, who joined the club in the summer, said
"It's exciting
It's going to be loud and it's going to be a very good day.
"There is a lot of emotion
It means a lot to people, the whole city
Football needs derbies like that.
"A lot goes into the game, it's not just going to the final
"I have experienced big matches before
I have fought for trophies before and it's the same problems you encounter going into them all.
"I know how to cope with the pressure and that's the most important thing."
Saturday's other semi-final will see holders Aberdeen continue their defence of the trophy when they clash with Dundee United at the national stadium.
Fixtures (1500GMT unless otherwise stated)
Saturday
Dundee United v Aberdeen
Sunday
Celtic v Rangers (1330)
Source : AFP
Source: AFP