Playing against the big-serving Croatian Marin Cilic, the seven-time Wimbledon champion looked in deep trouble at the end of the second set, after losing them both 7-6 and 6-4.
But the Swiss legend steadied himself and regained his composure to roar back at Cilic, winning the next two sets 6-3 and 7-6.
Federer then claimed the fifth and final set 6-3, in front of a jubilant and tense Centre Court crowd.
In the process, Federer created a slice of Wimbledon history, by winning his first match at the tournament from two sets down.
He’ll now face the Canadian Milos Raonic in Friday’s semi – with a tantalising final against Andy Murray still very much on the cards.
It wasn’t just those at Centre Court who were enthralled by Fed’s comeback – this lot enjoyed it too:
— Rahul Parasuraman (@Rahulparasu) July 6, 2016
If Federer wins his 18th Grandslam here then this is the day on which he really won it, mad comeback https://t.co/nINHWdp1R0
— Hernan Felivitto (@Vill2016) July 6, 2016
Never been the biggest fan of Roger Federer, but every time I watch him play, it's just pure greatness on display
— Jesse Parker (@The_Other_JPP13) July 6, 2016
— Matthew Bennett (@bennett_matt93) July 6, 2016
— MKEC (@erikacastro103) July 6, 2016
— Tishtriya (@tishtriya) July 6, 2016
— Deepak Kumar (@Deepakrdk1) July 6, 2016
— Manoj (@darringmanoj) July 6, 2016
I want Federer to win. Stuff Murray
— Adam Storey (@storey_a98) July 6, 2016
The greatness of Federer is that he pulls off something extraordinary that opponent can never anticipate coming #Wimbledon
— Pranay (@pranaytweets) July 6, 2016
Roger Federer proves once again why he's still (and forever will be) the greatest tennis player ever!
— Brooklyn bred (@truthguruisbad) July 6, 2016
Federer just showed wat a champion is made of #FedererVsCilic
— rakendu (@rakendur) July 6, 2016
So, can Federer, at the grand old age of 34, claim his eighth Wimbledon crown this weekend?
Let us know in the comments section below…