One thing is clear: a rivalry exists between these two clubs. It is certainly rather one-sided, Liverpool had not won against Real Madrid since 2009 before tonight, but the animosity is there.
From the off the two sides were nipping at each other's heels in what turned out to be a cracking match under the lights at Anfield.
Arne Slot's Liverpool started the stronger of the two sides and rarely looked back as they generated far more chances than the opposition.
They nearly took the lead after just four minutes as Darwin Nunez's shot was cleared off the line by Champions League debutant Raul Asencio. He is currently playing while under investigation for an alleged sex crime.
The chances kept coming for Nunez in the first half but Thibaut Courtois stood strong on several occasions to deny the Uruguayan a goal.
Alexis Mac Allister was the star of the match
Nunez's fellow South American Alexis Mac Allister scored the first goal for Liverpool. A quick one-two with Conor Bradley on the edge of the box before a neat finish into the bottom left-hand corner broke the deadlock that looked like sticking around until the end of the game.
Kylian Mbappe had a golden opportunity to equalize when Andrew Robertson conceded a penalty. However, Irish goalkeeper Coamhin Kelleher stepped up to deny the French superstar.
Mbappe's Champions League woes for Madrid continued tonight as he did not even manage a shot on target from open play.
It was only minutes later that Liverpool were awarded their own penalty but Mohamed Salah, who had a quiet game, put it wide.
Cody Gakpo, who often rises to the occasion, extended Liverpool's lead and sealed the win for the home side. He towered above the Real Madrid defenders to nod home a strong header and secure victory.
Real Madrid's European struggles deepen
It is not something that we have become accustomed to seeing in the Champions League but Real Madrid struggled once again against top opposition. They sit at the bottom of the playoff spots in 24th, precariously placed and at serious risk of being out of Europe altogether should their form in the competition fail to improve.
The wheels have just kept turning for Carlo Ancelotti at Madrid but it appears as if they might need a more serious reset.
Their next fixture against Atalanta could be incredibly tricky and might kick off the death spiral that could see Madrid fail to qualify for the knockout round for the first time in the history of the competition.
Liverpool, meanwhile, have taken a maximum of 15 points from their five games so far. They are beginning to emerge as the clear favorites to win the competition and their revitalization under Arne Slot has been nothing short of fantastic.
They were so good defensively that Kelleher only needed to make one save despite Madrid boasting some of the most firepower of any club in Europe.
The Reds take on Girona in their next game in a fixture that you would assume should be relatively routine.
