The Kzinti had a history of conflict with Earth, as the two planets fought a series of four wars between them. In what was collectively known as the Earth-Kzin Wars, Kzin was always the aggressor and Earth was always the victor. The first was fought sometime after First Contact in 2063, and the last was concluded by the end of the 2060s.
Following the signing of the Treaty of Sirius, the Kzin government, including all Kzinti territories, were essentially demilitarized. The Kzinti were forbidden to possess any sort of weapons or starships – except police vessels, which were to be used solely for peacekeeping.
Later that year, Kzinti archaeologists discovered two Slaver stasis boxes on Kzin. They turned one over to Starfleet to have transferred to Starbase 25; the second they kept for themselves, only to discover that it was empty.
Based on various lucrative finds in previously discovered stasis boxes, the Kzinti hoped to find a potentially powerful weapon, which they could use to defeat the Federation. Secretly supported by the Highest of Kzin, some privateers acquired a "stolen" police vessel to conduct their mission. If they were successful in their theft of the other stasis box, they would be heroes; if they failed, they would be repudiated by the Kzin government.
On stardate 4187.3, a group of Kzinti privateers lured the long-range shuttle Copernicus into the Beta Lyrae system, using the empty stasis box. They then captured the crew of the Copernicus on the surface of a barren ice planet, placing them in a police web aboard their privateer vessel, the Traitor's Claw.
Upon inspection of the stolen stasis box, the Kzinti discovered a Slaver weapon, whose functions they immediately began to test. By the time they reached the last function, the device, a sort of "smart computer", interpreted the Kzinti as enemies and self-destructed, killing three of the Kzinti privateers and severely damaging their vessel. (TAS: "The Slaver Weapon")
The Kzinti were large, carnivorous, cat-like beings that stood over two meters tall. Their anatomy was extremely well reinforced, as they possessed multiple hearts, and vertical braces along their ribs.
Some male Kzinti were capable of reading minds; however, psychologically, they were often unhappy and neurotic. Although there were no sure ways to prevent a Kzinti telepath from reading someone's mind, it was found that mental imagery of eating vegetation dissuaded them from making such attempts. (TAS: "The Slaver Weapon")
The Kzinti were a prejudiced, war-like species who often spoke of pride and honor. Males had no respect for males of herbivorous species, such as Vulcans, or of females of any species. This lack of respect stemmed from the fact that on their homeworld, Kzinti females were simply "dumb animals".
If a Kzin was defeated in battle but allowed to live, that action was considered the ultimate insult. In such a case, the Kzin had to seek revenge by challenging the attacker to a duel before the attacked Kzin was allowed to seek either medical assistance or reinforcements. (TAS: "The Slaver Weapon")
Unlike the other alien antagonists of Star Trek, the Kzinti species was an original creation developed independently of the television production, well before their 1973 TAS appearance. Science fiction author Larry Niven's Kzinti were introduced as part of his Known Space universe in The Warriors, a short story published in 1966.
According to The Worlds of the Federation by Shane Johnson, the Caitian homeworld is believed to be an ancient Kzinti colony. Caitians are however peaceful in nature contrary to their cousins. These data points reflect the information first published in M'Ress' biography by Lincoln Enterprises.
An interesting error occurred during production of "The Slaver Weapon". Director Hal Sutherland was red/green colorblind, and while he intended to colorize the Kzinti with green colors for their ship and uniforms, they ended up a pink and purple color.
Although Kzinti naming conventions were not explicitly discussed in "The Slaver Weapon", the naming conventions of the characters in the episode correspond to creator Larry Niven's descriptions of this in various stories. According to Niven, the Kzinti are not named at birth; they must earn their names through valorous deeds, typically ones that advance the interests of the Patriarchy. Unnamed Kzinti have lower status, and are referred to by the name of their profession, as was Telepath. Single-named Kzinti have distinguished themselves in some manner. They often follow their awarded name with the name of their profession, as did Chuft Captain. Kzinti can accumulate multiple names if they continue to perform valorously.
The Kzinti made no further appearance in Star Trek after "The Slaver Weapon", and a brief mention in "The Infinite Vulcan". The council of Elysia in TAS: "The Time Trap" had seemingly included a prototype, perhaps ancestral, Kzinti creature with the familiar bat-wing ears. A female felinoid seen in Star Trek V: The Final Frontier was referred to in backstage information as a "Kzinretti". "Kzinrretti" (with two "r"'s) is actually plural of "Kzinrret", the official term for Kzinti females.
It has often been said that an unseen species mentioned in the Star Trek: Deep Space Nine episode "The Adversary" – the "Tzenkethi", a near-anagram of "The Kzinti" – were supposed as a replacement. Robert Hewitt Wolfe said recently that he combined the name "Kzinti" with "Tsankth", a race from the RuneQuest and HeroQuest RPGs, in naming the Tzenkethi. Wolfe also notes that he did not picture the Tzenkethi as looking like the Kzinti, but as "heavily armored lizards".
The Kzinti also made brief appearances in the 1 March 1982 to 17 July 1982 Star Trek newspaper comic strip The Wristwatch Plantation by Sharman DiVono and Larry Niven with art by Ron Harris. The story involved Kzinti starting an invasion in the 2270s. The authors considered publishing the story as a novel or comic book,  but this did not happen.
In 2003 Jimmy Diggs tried to pitch a CGI animation adventure in feature length entitled Star Trek: The Lions of the Night in which the crew of the USS Enterprise-B under command of Captain Sulu was facing an invasion fleet. The project however didn't go very far, even though it had the support of Larry Niven and the Roddenberry estate.
It has been recently disclosed that if Star Trek: Enterprise had been renewed for a fifth season, Manny Coto wanted to do a Kzinti episode. Much of the concept for the episode "Kilkenny Cats" (which was based on a story by Neal and Jana Hallford) was to draw from the earlier concept Star Trek: Lions of the Night by Jimmy Diggs. D.C. Fontana and André Bormanis were also involved in the editing of the script.
To get the producers convinced a "rough rendering" of a Kzinti starship based on the movies era Dark Stalker was produced for possible use. The artist Josh Finney said that he was "...commissioned by writer Jimmy Diggs to design an Enterprise-era Kzinti cruiser as part of an overall pitch to Paramount." He further said "As for my ship design, truth be told, Paramount's people would've probably re-designed it a billion times before it hit the screen. But, still, I would've at least provided the starting point for the concept."
It is notable that the concept design of the Kzinti vessel draws considerably from the Kzinti fleet as presented in the Star Fleet Universe, which have a similar layout to the design shown, including the same triple warp nacelle layout and pod-mounted drone (missile) launchers. Jimmy Diggs did that on purpose, hence the three nacelles, but with more emphasis on creating a believable warship. The 2150s version combines aircraft and submarines of World War II (see here).
Kzinti in novels
Star Trek Log 5 by Alan Dean Foster begins with a flashback scene of M'Ress' career in Starfleet. Among one of the events is her time as a junior communications officer aboard the USS Hood: The starship was attacked by a Kzin cruiser, killing all of the bridge crew including the chief engineer, and crippling several systems including engines and communications. M'Ress, who speaks little Kzinti, volunteers to beam over to the cruiser which was disabled in the counterattack. The Kzinti are sending a distress call to their homebase which needs to be cut off and M'Ress' further plan is to recode it to send a distress call of their own to a Federation starbase. Her actions resulted in a promotion to lieutenant after just two years of service and the transfer to the Enterprise. The battle was mentioned in M'Ress' biography by Lincoln Enterprises where it is stated: "She entered Starfleet just three years ago", placing the event in 2266.
The Pocket TOS novel Ishmael by Barbara Hambly contains a throw-away line to the Kzinti: The Starbase's commanding officer, Maria Kellogg, served as chief engineer of the USS Republic before in her career. She was one of six Human crewmembers, the rest were Orions, Kzinti and Trisk. (Revealed in Chapter 7; story might be set during end of the five-year mission.) Later Kellogg and Kirk pass two Kzinti in the corridors of the station. Kellogg greets them in their native tongue. (Revealed in Chapter 13.)
Kzinti appear within Star Trek Online renamed to Ferasan while maintaining a close resemblance to Caitians in appearance. They are also a playable race, can be recruited as non-player character crew members, and feature a small sidequest series further elaborating on their story and the Caitians'.
Kzintis in the Star Fleet Universe
The Kzinti race in the Star Fleet Universe – who have traits setting them apart from other continuities (cat ears, sentient females, Kzinti/Kzintis as singular/plural, etc.) from the Kzin of Niven's works – has fought wars with all of their neighbors, the Federation, the Klingon Empire and their perennial nemesis, the Lyran Star Empire. They are long-standing allies – or more accurately, co-belligerents – of the Hydran Kingdoms.
The Kzinti Hegemony eventually formed a tentative accord with the Federation, and allied with them in the General War, but they have been involved in major wars with the Klingons and Lyrans, such as the Four Powers War and the General War itself, in which a substantial region of their territory was occupied by their Coalition enemies and two full-scale assaults were made on the Kzinti homeworld of Kzintai.
Eventually with Federation assistance they forced the Coalition forces from their territory, but after the war ended they were involved in a civil war as a disgruntled faction – which had been opposed to the Hegemony's ruling patriarch and sought refuge and developed a power base in the WYN Cluster, and launched an attempted coup of the Hegemony itself in the WYN War of Return.
Also, in the fictional variant of the Star Fleet Universe as represented in the games Star Trek: Starfleet Command II: Empires at War and Star Trek: Starfleet Command - Orion Pirates from Taldren, the Kzinti were renamed and re-interpreted as the more canine Mirak.