Celtic, the Scottish champions-elect, have already beaten fellow Glasgow giants Rangers three times this season but lost to them in an Old Firm clash at the same stage of the Scottish Cup last term, with the Gers then in the second-tier Championship.
That penalty shoot-out loss, following a 2-2 draw, played a major part in ending Ronnie Deila's time as manager of the Hoops, with former Liverpool boss Brendan Rodgers now in charge at Parkhead.
Hibernian, however, won the Cup last season and the Edinburgh club will be up against an Aberdeen side who are second in the Scottish Premiership.
Edinburgh-based Hibs are now in the Championship but they have an excellent recent Cup record after appearing in the semi-finals in each of the past three seasons, with last year's success ending a 114-year wait for a third Scottish Cup triumph.
Celtic had to come from behind to beat St Mirren 4-1 in the quarter-finals on Sunday, with Aberdeen seeing off Partick Thistle 1-0 thanks to a Graeme Shinnie goal at Pittodrie in the day's other tie.
Hibernian were 3-1 winners over Ayr on Saturday while Rangers thrashed Hamilton 6-0.
"It is a good draw and I think Hibs will see it exactly the same way as we do," Aberdeen manager Derek McInnes told the BBC on Sunday.
"If we are all being honest, I think the three other teams would have wanted to avoid Celtic because they are the strongest team at the minute."
Celtic boss Rodgers, meanwhile, said he was delighted how his team fought back to beat lowly St Mirren after going a goal behind.
Jack Ross' side lie five points adrift at the bottom of the Scottish Championship but they belied their lowly status as they gave the runaway Premiership leaders an early scare when Harry Davis handed the Buddies a shock lead in the 13th minute.
However, two Celtic goals in two second half minutes quickly turned the game on its head as Mikel Lustig headed home a 58th minute equaliser before Scott Sinclair fired the Hoops in front.
Moussa Dembele knocked in his 32nd goal of the season with substitute Leigh Griffiths grabbing a fourth to ensure Celtic remain unbeaten in 34 matches this season.
"I thought it was a great performance by us in the second half. I give a huge amount of credit to our players," said Rodgers.
"We weren't so good in the first half. We were just a bit below our tempo but we stayed calm and in the second half we just upped the tempo a little bit.
"Of course as games go on for us the fitness and mobility in our team really comes through so we know we're going to create chances. It's then about taking them and just making sure we were stable."
Scottish Cup semi-finals
Celtic v Rangers
Hibernian v Aberdeen
Ties to be played at Hampden Park on the weekend of April 22-23