Celtic took a huge step towards a return to the Champions League with stunning goals from Benjamin Nygren and Camilo Duran.
Derek McInnes described Lawrence Shankland as a "brilliant" captain who will have a "big influence" at Rangers whether or not he starts games.
Rangers have signed right-back Kosta Nedeljkovic from Aston Villa.
Martin O'Neill believes Celtic should "aspire" to win the Champions League ahead of their play-off round qualifier against Austrian champions LASK.
"I will be one of yours and I will do my best to make the supporters smile."
Scotland have appointed Sebastien Pocognoli as their new head coach.
A round-up from the Scottish League Cup as Celtic eased through to the quarter-finals with 4-0 victory at Dundee United, Aberdeen beat Dundee, Kilmarnock won against Ayr United, while League One Ross County shocked Dunfermline.
Derek McInnes earned his first win as Rangers manager with a dominant 5-1 victory over holders St Mirren to advance to the quarter-finals of the Scottish League Cup, where they will meet rivals Celtic.
"Derek McInnes is doing the best that he possibly can with what's at his disposal to try and get results."
Celtic manager Martin O'Neill says he is disappointed to be losing Arne Engels to West Ham, but accepts it is a move he has to make.
Derek McInnes admitted Rangers are "not ready" to compete at Europa League level.
Derek McInnes' winless start to life at Rangers hit its lowest point as they were embarrassed and dumped out of the Europa League to a chorus of boos by Jagiellonia Bialystok on aggregate following a 1-1 draw at Ibrox.
Celtic have made their fourth summer signing with midfielder Mika Baur joining on an initial four-year deal, with the option for a further year.
Derek McInnes believes Rangers are "playing with fire" after being left with a shortage of options in defence.
Celtic have announced the signing of winger Haissem Hassan from Real Oviedo in a potential £9m move.
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Rangers have completed the signing of winger Daisuke Yokota from Hannover 96.
Four days, six matches, 18 goals, and one opening weekend full of unmissable drama.
Celtic will play Austrian champions LASK for a place in the league phase of the Champions League, while Brighton will face CFR Cluj or Tromso in the Conference League play-off round.
Celtic made a winning start to their Scottish Premiership title defence with a 1-0 victory over battling Dundee at Celtic Park.
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