Berrettini makes history by reaching Australian Open semi-finals
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The seventh seed overcame the French 17th seed in their quarter-final 6-4, 6-4, 3-6, 3-6, 6-2 to become the first Italian man to reach the last four of the Australian Open.
Berrettini, a Wimbledon finalist last year, will now face 20-time Grand Slam champion Rafael Nadal on Friday for a place in Sunday's final.
"It feels unbelievable (to be the first Italian), hopefully there will be a second one tomorrow with Jannik Sinner," Berrettini said of his compatriot, who faces Stefanos Tsitsipas in a quarter-final on Wednesday.
"I was really happy with myself, it was a great fight with Gael, a great match, a lot of emotions.
"I thought I had him in the third set but then I found myself in the fifth. I really fought hard and I put everything into the court."
In a grinding 3hr 49min night match on Rod Laver Arena, 25-year-old Berrettini grabbed a double break to surge clear in the fifth set after Monfils had roared back from two sets down.
It was Berrettini's sixth win in seven career five-set battles.
There were many drawn-out, attritional games, including a monumental 20-minute Berrettini service hold game of 10 deuces to give him the edge in the 62-minute second set.
It means the 35-year-old Monfils, who won the warm-up Adelaide tournament and had not dropped a set in his previous four matches, came up just short again in his first quarter-final appearance in Melbourne since 2016 when he lost in four sets to Canada's Milos Raonic.
Monfils credits his recent resurgence to the stabilising influence of his new wife, women's world number 17 Elina Svitolina. The tennis "power couple" tied the knot in Geneva in July just before the Tokyo Olympics.