There was a time when New Zealand were the most feared team anywhere in sport, never mind rugby.

But little by little, Ireland have chipped away at the All Blacks' armoury and go into Saturday's quarter-final with not just hope, but with a realistic chance of toppling New Zealand on the sport's biggest stage.

BBC Sport takes a look at the landmark wins that moved Ireland from huge underdogs to equals at the top table.

2016 - Home run in Chicago - Ireland 40-29 New Zealand

Once upon a time, when you stepped out against New Zealand and the Haka took place, there was almost a feeling that a team would be down on the scoreboard before a ball was kicked.

Ireland knew that feeling more than most, and despite coming agonisingly close to taking that breakthrough win in 2013 before Ryan Crotty's last-gasp try, overcoming New Zealand was a mountain they could never scale.

Something felt different in November 2016 when a historic match was set to take place at Soldier Field in Chicago - on the same weekend the Cubs won Baseball's World Series.

From the start, the Irish effort appeared to be fuelled by the memory of former international and Munster head coach Anthony Foley, who had died suddenly the previous month. Prior to kick-off Ireland lined up in the shape of a number eight, the jersey worn with distinction by Foley for many years, while their opponents performed their traditional pre-match Haka.

Tries from Jordi Murphy, CJ Stander and Conor Murray helped Joe Schmidt's side to a 25-8 half-time lead, then Simon Zebo scored his side's fourth try in the corner.

The world champions fought back to move to within four points but Robbie Henshaw's late score ensured the victory. It took 111 years, but Ireland had finally got the job done.

2018 - Home comforts in Dublin - Ireland 16-9 New Zealand

New Zealand hit back to triumph in Dublin just two weeks after the Chicago game, but two years on at the Aviva Stadium, it was Ireland's turn to roar.

Jacob Stockdale's now-iconic try was the highlight on a famous night, with his chip and chase coming off to perfection to send the Irish support into raptures.

Johnny Sexton kicked the rest of Ireland's points, making amends for a painful missed penalty in the heartbreaking 2013 defeat.

As you would expect, New Zealand came hard and heavy as they looked to hit back, but Ireland were so impressive they managed to stop the visitors scoring a try, with Beauden Barrett kicking their nine points.

Another milestone reached. Another box ticked.

2022 - Mentality monsters - New Zealand 22-32 Ireland

Winning on home turf is one thing (and although Chicago was 'neutral' it may as well have been in Dublin given the swell of Irish support in the USA), but victory in New Zealand is an entirely different prospect.

After their previous wins - although New Zealand had their victories since 2016 which included a thumping 46-14 World Cup quarter-final win in 2019 - there was a feeling that Ireland's three-game tour last year was going to be massive for Andy Farrell's squad.

It looked like that hope was misplaced when four tries in 17 first-half minutes helped New Zealand emphatically preserve their remarkable 28-year unbeaten run at Eden Park with a six-try win.

However, Farrell's men hit back as Andrew Porter scored a try in each half to help Ireland secure that historic 23-12 first win on Kiwi soil after the All Blacks were hit by Angus Ta'avao's red card.

There was better to come. In the deciding Test Ireland produced a near-faultless first half to open up a 19-point lead in Wellington.

New Zealand hit back but Rob Herring's try gave the Irish the breathing room required to see the game out and secure a first series win.

The emotion etched across the players' faces said it all, and there was a feeling that this was much more than a Tour victory.

It was one of the greatest achievements in Irish rugby history - but this group wanted more.

2023 - The next chapter? - World Cup quarter-finals

Now Ireland have only one hurdle left if they are to banish the All Blacks' aura - and it's a big one.

Farrell's men will be looking to create more history with a first win over the All Blacks at the World Cup.

Saturday's World Cup quarter-final is a chance to prove that Ireland have eradicated the All Blacks' fear factor as they go in pursuit of their ultimate dream.

It comes four years after the All Blacks annihilated Ireland in the last eight in Japan, but now Farrell's side are in a far better position to deal with New Zealand's threat.

However, you can never write the Kiwis off and there's a lot at stake as the two rugby heavyweights battle it out for a place in the semi-finals - a place Ireland have never ventured before.

There have been plenty of new landmarks in recent years, will Saturday's chapter provide another? It all comes down to this.