The controversial Liverpool striker has been in hot water for biting opponents (twice!), for killing the hopes of underdogs with flagrant handballs (twice again!), and for his behaviour in racially abusing Manchester United's Patrice Evra, before denying it, then failing to shake his hand the next time they played each other.
The video sums up those misdemeanours, although there are plenty of others, such as violent conduct while playing for Uruguay, taking a former club to court to force a transfer, and a reputation for diving, which is not very popular with British fans.
Take your pick - and let us know whether you think Arsenal should break the bank sign this gifted but flawed genius...
Suarez's rap-sheet in pictures...
1. The hand of God (June 2010) - Suarez denies Ghana a historic appearance in the World Cup semi-finals by deliberately handballing off the line. Ghana miss the penalty, and Uruguay reach the semis on spot-kicks, with Suarez unrepentant afterwards.
2. The hand of God pt 2 (January 2013) - Suarez handballs his side through again, this time for Liverpool against lowly Mansfield in the Cup.
4. The Cannibal of Liverpool (April 2013) - The pattern of a repeat offender continues, as Suarez bites Chelsea defender Branislav Ivanovic. Taking into account his record, he is banned for 10 matches.
5. Suarez racially abuses Evra, admits it, claims he was being friendly, accuses FA of bias (October 2011) - The title says it all. Suarez insisted the word he used while addressing Evra is a term of endearment in his native Uruguay despite having lived in Europe for five years at that point. He was banned for eight matches.
6. Suarez refuses to shake Evra's hand (February 2011) - Evra eventually apologises but then snubs Evra in the traditional pre-match handshake.