Kylian Mbappe's hat trick against Manchester City propelled Real Madrid into the Champions League last 16 on Wednesday and saw the French superstar reach a new personal high with Los Blancos.

This was the kind of night Mbappe dreamed of, both as a boy in his bedroom surrounded by Cristiano Ronaldo posters and in his past few seasons at Paris Saint-Germain.

As PSG came up short year after year in Europe, Mbappe watched as Madrid extended its dominance over the European game, reaching a record 15 European Cup triumphs.

With Madrid's poor start to the current campaign — in part due to Mbappe's teething problems — leaving the reigning Spanish and European champion in the playoff round against City, it needed the forward to deliver.

He did just that with three lethal finishes to help Carlo Ancelotti's club seal a 3-1 win on the night and a 6-3 aggregate triumph.

"This is the type of game we want to play," Mbappe said.

"People told me about these nights, and now I can see it with my own eyes, and I want to live through many more of them."

After years of speculation and failed attempts, Mbappe finally arrived in the Spanish capital last summer.

However, his first few months brought problems, an apparent lack of confidence and erratic form.

Missed penalties against Liverpool and Athletic Bilbao highlighted the concerns around him, but Mbappe drew a line under them and pledged to show his character.

With 18 goals in his last 18 matches, he has done just that, and his best performance in a Madrid shirt came at the adoring Santiago Bernabeu against City.

"I knew that I couldn't have done worse than I was doing," Mbappe said after his stunning treble against City.

"I had to play with personality, my adaptation time was over, and I have to show my quality."

Mbappe said signing for Madrid to accomplish his long-term goal was not enough.

"Making my dream come true is one thing, but I want to play well here, mark an era and write history at Real Madrid," he explained.

"I've always said I have no limit, if I can score 50 goals, I will score them, if I can score more, I'll score more, but the important thing is winning titles.

"In my career I've scored a lot of goals, but we have to see if they mean something, because in the end we didn't always win titles ... if I can score a lot of goals, and we win the trophies, I'll sign for that with my blood."

Mbappe has 28 goals for Real Madrid in 38 games, and the form he is in has opened comparisons to the club's all-time greats, even though he is just at the start of his tenure.

"He has the quality to reach the level of Cristiano (at Madrid)," Ancelotti told reporters.

"He has to work because Cristiano set the bar very high, (Mbappe) has just started at this club.

"For the quality he has, and the excitement he has to play here, he can reach Ronaldo's level, but it won't be easy for him, he has to work."

Portuguese veteran Ronaldo scored 450 goals in 438 games for Madrid after joining from Manchester United in 2009, becoming the team's all-time top scorer.

Mbappe's childhood idol departed Madrid in 2018, and although Vinicius Junior stepped up to become the team's key player since then, Mbappe's capacity for goalscoring means he is the player most likely to deliver on a similar scale.

Madrid will face city rival Atletico Madrid or German champion Bayer Leverkusen in the next round, and Mbappe said he would prefer a derby clash.

"Both would be difficult games, so it's better to have a difficult game without having to travel," Mbappe said.