Craig Levein’s men are favourites due to their Premiership status with John Robertson’s highland side sitting fourth in the Championship.
Hearts reached this stage after a welcoming run which saw they defeat Livingston and Auchinleck Talbot at Tynecastle before being drawn with Partick Thistle in the quarter final. A drew at Firhill meant a replay was in order with the team coming from behind to progress past the Jags.
Inverness had a more tumultuous time getting to the semi-final. They required two chances to see off Edinburgh City and Highland rivals Ross County. Sandwiched between those ties was a comfortable 4-0 victory over East Kilbride. They defeated Dundee United at Tannadice in the quarter final.
ICT have drawn 13 league games this campaign which has hampered their push at the top of the table but are well placed to finish in the end of season playoffs.
It is the third time the clubs have met at the last-four stage in Scottish cup competitions.
In consecutive seasons the teams faced each other in the League Cup final at Easter Road. In 2013 Hearts emerged victorious with a 5-4 win on penalties after a 1-1 draw in normal time. They did so despite playing the whole of extra time with ten men.
The following year Inverness got their revenge, this time winning on penalties after a 2-2 draw. It was made all the more special given the fact they played all of extra time with nine men.
Here’s what fans need to know about the Hampden clash:
What time is kick-off?
It is an early start with a 12.15 kick-off. The timing of the match angered Inverness chairman Graham Rae.
He said: “I don’t know how much say we will have, particularly as the minnows among the four clubs in the semi-finals. We want the best set of circumstances for our supporters and our club.”
How many tickets have been sold?
Is the game live on TV?
If you are unable to make the game you won’t miss out with it being available to view live.
What channel is it on?
In November last year the Scottish FA agreed a new £20million six-year deal with BBC Scotland and Premier Sports to broadcast the competition.
This semi final be available on both BBC Scotland and Premier Sports 1.
What time does coverage start?
The build-up to the game will be five minutes on Premier Sports with the programme starting at 12.10.
As of yet, there is no schedule available for BBC Scotland.
The competition’s sponsors William Hill have Hearts as overwhelming favourites.
Hearts 1/2 Draw 11/4 Inverness CT 5/1
To win the Scottish Cup the Edinburgh side are 3/1 second favourites, while the Highlanders are 16/1 to pick up the trophy they did in 2015.