The Reds forward is currently in the form of his life, scoring 17 goals in just 11 Premier League appearances as his club have climbed impressively to second place in the table, from where they could reach top spot on Saturday.
The Uruguayan―who on Monday night was a humble winner of the Football Supporters' Federation Player of the Year award (Daily Telegraph)―has mixed success, failure, controversy, even more controversy and an awful lot of goals during his time wearing red, but which moments and matches stand out?
Here we tell the story of Suarez's time in England through 15 memorable matches.
The Anfield crowd had to wait until just over an hour into the game against Stoke City for a glimpse of their new star man, but when they got it, it was a memorable one.
A frantic transfer deadline day at Anfield had seen Fernando Torres exit for Chelsea and Suarez and Andy Carroll arrive, but Carroll was injured and the Uruguayan wasn't considered ready to start against Tony Pulis' Stoke after just a couple of days in England.
It meant that Kenny Dalglish's men lined up with Dirk Kuyt upfront supported by Raul Meireles and Steven Gerrard, a tactic that wasn't working too well until Meireles fired the Reds in front early in the second half.
Then, enter Suarez.
The forward replaced Fabio Aurelio in the 63rd minute, and took just 16 minutes to make his mark when he raced on to a Kuyt pass, rounded goalkeeper Asmir Begovic and found the net via an attempted clearance from Andy Wilkinson onto the post.
He had arrived.
Suarez was still getting used to life in England when he was pitched into arguably the country's biggest matchup the following month.
Manchester United were top of the league when they came to Anfield in early March of 2011, but that didn't faze Suarez and Liverpool, who were convincing winners on the day.
One of the reasons for that was their Uruguayan forward, who set the match alight in the 34th minute when his staggering close control saw him ride several United challenges before prodding the ball across the goal line for Kuyt to tap in.
The Dutchman scored again before the break, and then completed his hat-trick when a Suarez free-kick was fumbled by Edwin van der Sar, allowing Kuyt to tap home from close range.
Javier Hernandez pulled a late goal back for United, but there was little doubt that it was Liverpool's day thanks to Suarez and Kuyt.
Seven months later, it was another visit from United which turned into one of the defining moments of Suarez's career.
An always hotly contested affair erupted early in the second half when Suarez clashed with United full-back Patrice Evra in front of the Kop.
At the time it looked to be a run-of-the-mill argument on the football pitch, but after the match―which ended 1-1 following goals from Gerrard and Hernandez―an accusation was made that Suarez had racially abused Evra.
Whilst the case was being investigated the forward played in 10 more league matches―picking up a one-match ban for an abusive gesture to fans following a defeat at Fulham, before Liverpool's players and manager Dalglish infamously wore t-shirts defending him from the Evra charge in a game at Wigan following the FA's decision to ban him for eight matches pending an appeal.
On January 3rd 2012, the day of a match at Manchester City, Suarez accepted the verdict and as well as the eight-match ban, was fined £40,000.
As someone who never seems to do anything quietly, Suarez's comeback from the ban was always going to be headline news.
He'd appeared from the bench in a home game against Tottenham earlier in the week, and promptly accidentally kicked Scott Parker in the chest to spark a flurry of sensationalist calls for a red card from many, including Wayne Rooney (Metro).
The headline act was always going to come at Rooney's Old Trafford five days later though, and sure enough the refusal of a handshake between Suarez and Evra before the match set the tone for a poisonous afternoon and aftermath.
United won the game thanks to Rooney's two goals to Suarez's one, a result that prompted Evra to leap around in celebration in front of Suarez as the players walked off at full-time.
With the incident becoming increasingly messy, Liverpool's owners were believed to have stepped in (BBC) in an attempt to calm things down, an act that ultimately ended in an apology from both Suarez and Dalglish.
Two weeks after that Old Trafford loss, Liverpool took on Cardiff City in the League Cup final at Wembley and promptly squeezed home a victory on penalties to give Suarez a first trophy in England.
A couple of months later though, there was an even bigger game at the national stadium.
The Reds and Everton had made it to the semi-final of the FA Cup, and they took each other on in front of a packed crowd which appeared to include the whole of Merseyside.
Everton started the better and took a deserved first half lead through Nikica Jelavic, but Suarez turned the tide in the second half.
Pouncing on a dreadful backpass from Sylvain Distin, the forward powered into the box and fired Liverpool level in front of the ecstatic Reds supporters, before Suarez's strike partner Andy Carroll headed home a priceless winner three minutes from time.
Liverpool were going back to Wembley.
This was a pretty good way to prepare for an FA Cup final.
League form had taken a back seat as the Reds prepared to face Chelsea in the Wembley showpiece, but a week earlier Suarez displayed his staggering talents to shoot down Norwich City single-handedly. It wouldn't be for the first time.
Suarez produced two craftsman's finishes in the first half to put the Reds two up, before he capped things off with a remarkable lob over goalkeeper John Ruddy from around 50 yards out to complete his first ever Liverpool hat-trick.
Norwich were going to become opponents he enjoyed facing.
A week later though, and there was despair for Suarez and Liverpool.
The Reds were second best against Chelsea in the FA Cup final at Wembley, going a goal down when Brazilian midfielder Ramires strode into the box to fire past Pepe Reina, before Didier Drogba made it 2-0 in the second half.
Suarez had been isolated for much of the game, but things improved for Liverpool when Carroll came on and almost instantly blasted his club back into the game, with only a stunning late save from Petr Cech denying the big Englishman an equalising goal with a point-blank header.
Chelsea held on for a 2-1 win just two weeks before they would become European champions, ensuring that it was a miserable day for the Reds and their No. 7.
Two cup final appearances couldn't save Dalglish his job, and Liverpool appointed Brendan Rodgers as their new manager in the summer of 2012.
The Northern Irishman knew that he had a huge task on his hands, but he decided that Suarez was going to be central to it. He agreed to loan Carroll out to West Ham and make the Uruguayan his central striker―a decision that he has been talking about recently (Guardian).
Things didn't start smoothly though, with no wins in the first five matches of the Premier League season ensuring that Liverpool went to Norwich in late September in the relegation zone.
Luckily for them though, Suarez was facing his favourite opponents.
The forward scored his second Carrow Road hat-trick in the space of five months, with Nuri Sahin also finding the net along with a Leon Barnett own goal as Liverpool won 5-2.
The season had finally begun.
Maybe Suarez was finally learning to laugh at himself.
Before last October's Merseyside derby at Goodison Park, then Everton boss David Moyes sought to ramp up the pressure on the forward and the officials by discussing Suarez's apparent desire to go to the ground too easily (Sky Sports), something that he would later admit to doing in a match against Stoke City which had taken place earlier in the season (Guardian).
Clearly Suarez didn't think too much of Moyes's words, and after his fierce effort bounced into the net off Leighton Baines, he celebrated by taking an elaborate dive in front of the Blues manager.
Suarez then scored again to put Liverpool two up, but Everton rescued a point through goals from Leon Osman and Steven Naismith with home captain Phil Neville later booked for diving, embarrassingly for his manager.
One week on, Suarez scored what many have regarded to be his best goal in a Liverpool shirt, but one which has picked up some competition in recent weeks.
The Reds trailed to a Yohan Cabaye goal against Newcastle at Anfield when Suarez struck midway through the second half.
A pinpoint pass from left-back Jose Enrique was expertly taken on the forward's chest in front of the Kop, which then watched on as Suarez―seemingly with the ball tied to him on a string―navigated his way around Fabricio Coloccini and Tim Krul before almost walking the ball into the net.
It was a moment of sublime brilliance from a player who specialises in them.
Many claim that the Europa League doesn't matter, but the look on Suarez's face after all of his remarkable effort failed to turn around last season's tie against Zenit St Petersburg spoke volumes.
The forward had missed chances in Russia as the Reds had lost 2-0, and an error from Jamie Carragher allowed Hulk in to widen that gap at Anfield. Liverpool now needed to score four.
Yet a low Suarez free-kick and a Joe Allen goal got them halfway there, and Suarez then scored a stunning free-kick from further out at the Kop end to give Liverpool half an hour to grab an extra goal and go through.
Try as they might though that just didn't happen, and after one of the great comebacks of Liverpool's history was narrowly missed out on, Suarez was disraught at full-time.
Just when it looked as though the forward was finally settled and that whatever demons he had were leaving him alone, Chelsea visited Anfield in April.
It was a match that was supposed to be all about ex-Reds boss Rafael Benitez returning to Anfield as he looked to guide the Blues to the Champions League, with Oscar's header giving Chelsea a half-time lead.
Daniel Sturridge―who had left the Londoners in January―equalised from a fine Suarez cross, only for the Uruguayan's handball to gift Chelsea a penalty, which was converted by Eden Hazard. Then came the moment the match would be remembered for.
As he tussled with Branislav Ivanovic as both prepared for a Steven Gerrard cross, Suarez inexplicably sunk his teeth into the Chelsea defender's arm. It was moronic and self-destructive.
Typically, he scored a 97th minute equaliser to ensure a 2-2 draw, but afterwards Liverpool were straight on the case and eager to avoid the PR disaster that was the Evra episode.
The club criticised Suarez―who had performed a similar act at Ajax before he left for Liverpool―and he was eventually banned for 10 games by the FA.
Many thought he'd never play for the Reds again.
He very nearly didn't.
After a summer-long saga which saw him linked to Real Madrid and most strongly with Arsenal (Daily Telegraph) it appeared certain that Suarez was going to depart Liverpool, and he even pleaded to be allowed to (BBC).
However, Liverpool stayed admirably strong on the matter, with the Reds refusing to sell their star man to anyone and simply looking forward to his return from his ban.
He came back, typically, in a League Cup match at Old Trafford, but it was his return to Premier League combat at Sunderland that was always going to be considered more important. He didn't disappoint.
Dovetailing expertly with Sturridge, the Uruguayan scored two and the Englishman one as the Reds won 3-1 on Wearside.
Against all the odds, their star man was back.
As he approached peak form, Suarez was simply blowing opponents away.
A strike at home to Crystal Palace followed on from that Sunderland goal, before the forward scored a magical hat-trick to see off West Brom at Anfield.
His first followed a clever run and trademark nutmeg on Jonas Olsson, before a remarkable header from the edge of the box from an Aly Cissokho cross and then another header from Steven Gerrard's free-kick.
Sturridge scored a late chip in a 4-1 win, but this was Suarez's day as he scored a first hat-trick at Anfield.
It is doubtful whether Anfield has seen a better striking performance for years.
Suarez was simply superb in scoring four goals against his favourite opponents Norwich earlier this month, strikes which took his tally to 11 in four games against them.
It was the quality of the goals which stood out here though.
A stunning 40 yard lob, a clever finish from a corner, a fierce half volley following a fine run and a 25-yard free-kick had Anfield up on its feet in a 5-1 win, and established Suarez as the finest forward currently plying his trade in England and one of the finest on the planet.