Katya Kazanova was a former love interest of Sterling Archer.
Katya was originally part of the KGB. When she was given a photo of Archer as a way of identifying their number-one enemy. Unfortunately, Katya was smitten.
After defecting from the KGB with Archer, Katya fell to her death protecting him from Barry Dylan. She was later rebuilt as a cyborg. She would eventually become head of the KGB as her previous superiors had all been killed.
Afer saving Archer from the KGB, he repaid her by offering protection. Katya was obviously a good influence on Archer, convincing him to give up drinking and being a better person. Both Lana and Mallory were suspicious, but Archer just chalked that up to jealousy. Archer proposed to Katya, knowing her to be his one true love, only to watch her die saving his life.
When Katya came back, she tried to rekindle her relationship with him. When the two are about to be married, Archer catches her sleeping with Barry. Remembering how he did something similar to Barry, Archer decides to let her go.
When Katya reconnects with Archer following Barry getting stranded on a space station, Archer plays along in the hopes that Katya's feeling for Barry would eventually go stale and she would fall back in love with Archer. The plan worked a little too well and Barry came back to Earth.
The next time Katya met Archer, he was going steady with Lana. Katya tried to seduce him, but Archer managed to resist despite her best efforts. Katya did almost jeopardise the relationship by leaving a detachable part of herself in their bathroom sink, which caused Lana to jump to conclusions.
After Barry was turned into a cyborg, he got revenge on Archer (who had slept with his girlfriend at one point and broke his bones twice) by killing Katya, albeit accidentally. Barry came after Archer on their wedding day, fighting the now-cyborg Katya. The two then sleep together, finding some connection due to the fact they were both cyborgs. Katya doesn't truly love Barry, as she was visibly uncomfortable leaving Archer for him. Barry similarly was only with Katya as a way of getting back at Archer.
Katya urged Barry to put his hatred of Archer behind him, but Barry goes behind her back and tries to attack Archer while on a space station. Archer manages to escape and destroy Barry's spacecraft, stranding him there for several months. When he finally escapes, Katya has taken over the KGB and uses her newfound authority to cow Barry once and for all. Their relationship has well and truly lost any semblance of romance it may have had and Barry is now little more than Katya's flunkie. Eventually Katya breaks up with Barry.