More than 100,000 fans are expected to attend this weekend’s matches and both games are also exclusively live on BT Sport.
Heart of Midlothian v Celtic – BT Murrayfield, kick-off 1.30pm
Road to the semis: Hearts topped Group C then beat Dunfermline Athletic 1-0 at East End Park in the last 16. They got past Motherwell 4-2 at Tynecastle to reach the semi-finals for the first time since 2013/14. Celtic beat Partick Thistle 3-1 at Firhill in the second round and a Leigh Griffiths goal was enough to see off St Johnstone 1-0 at McDiarmid Park in the quarter-finals.
League Cup pedigree: Celtic have won the trophy in each of the last two seasons and have claimed the cup 17 times overall. Hearts are four-time League Cup winners but their most recent success was back in season 1962/63 when Tommy Walker was their manager.
This season: Hearts won 1-0 at Tynecastle in August with a Kyle Lafferty goal and the teams meet again at Celtic Park next weekend.
Team news: Celtic defender Dedryck Boyata is suspended and Hearts forward Craig Wighton is cup-tied after playing for Dundee in the group stage.
In the event of a draw: Extra time and, if necessary, kicks from the penalty mark will settle the outcome if the scores are level after 90 minutes.
Referee: Willie Collum
Aberdeen v Rangers – Hampden Park, kick-off 4.30pm
Road to the semis: Aberdeen beat St Mirren 4-0 at Pittodrie in the second round and knocked out Hibernian on penalties after a 0-0 draw in the quarter-final at Easter Road. Rangers beat Kilmarnock 3-1 at Rugby Park then saw off Ayr United 4-0 at Ibrox to reach this stage.
League Cup pedigree: Rangers have won the competition a record 27 times but their most recent success was in 2010/11. Aberdeen are six-time winners of the League Cup and last got their hands on the trophy in 2013/14 when they beat Inverness CT on penalties at Celtic Park.
This season: It finished 1-1 at Pittodrie on the opening weekend of the Premiership season and the teams meet again at Ibrox on Wednesday December 5.
Team news: Rangers striker Alfredo Morelos is suspended and Kyle Lafferty is cup-tied after playing for Hearts earlier in the competition.
In the event of a draw: Extra time and, if necessary, kicks from the penalty mark will settle the outcome if the scores are level after 90 minutes.
Referee: John Beaton