Holders Celtic take on Kilmarnock in the first semi-final on Saturday at Hampden Park, with a 5.30pm kick-off, while Rangers face Aberdeen on Sunday at 3.00pm.
Celtic claimed the trophy last season after beating Hibernian 2-1 in the decider while Rangers have won this competition more often than anyone else.
Aberdeen have won the League Cup six times, most recently in 2013/14, while Kilmarnock's only success came against Celtic in the 2011/12 final.