He was captured during a raid of the warehouse that served as the headquarters of his cult. He attempts to summon a demon which is killed by Michael Carpenter. He later committed suicide in his jail cell before his trial and returned as the Nightmare.
In the series
In Grave Peril, Susan Rodriguez asks Harry Dresden if he recalls the name of the guy that he and SI took down a couple of months earlier—the ritual killer. He reaches for the name saying Leo something, Cravat, Kraven the Hunter or something. Dresden had tracked him down through the demon he called up. Dresden never really heard the name. Susan then asks if it was Kravos, Leonid Kravos, and Dresden agrees that was it. He is described as having brown hair going grey and an untrimmed beard.
Later, Dresden has a dream that recalls how he, Michael Carpenter and the Special Investigations took him down during a raid of the warehouse. Then the dream changes to an entirely different horrifying outcome in which the team is overtaken by the demon—Azorthragal—that Kravos summoned up and takes a huge bite out of Dresden.
Carpenter brought Lydia to Harry Dresden's apartment; he recognized her from Kravos's lair. When Lydia wakes up, she is possessed by the Nightmare. Carpenter can not slay it with Amoracchius because its inside Lydia—an innocent—not a construct and shedding innocent blood would undo the Sword. Just as Dresden is about to die, he finally realizes that Lydia is possessed by Kravos's ghost not his demon and knows how to destroy it. Thomas Raith distracts Lydia by using his White Court powers. This frees Dresden to exorcise Kravos's ghost from Lydia.
Later, locked in a room at Bianca St. Claire's mansion, Kravos inhabits Justine and taunts Dresden. shortly after, Dresden sets a trap for him, goes to sleep, Kravos enters his mind, Dresden dies, creates a ghost and destroys Kravos, eating back his powers and some of Kravos as well. Susan had been keeping his body going with CPR. After that, Dresden was strong enough to escape their prison taking Susan and Justine with him. 
In Summer Knight, Karrin Murphy is having continual bad dreams—night terrors—about what Kravos did to her. What scares her is that there wasn't anything she could do to stop his invasion of her mind.
In Ghost Story, Harry Dresden warns Murphy that with Mortimer Lindquist having been abducted by the Grey Ghost, he's not around to keep the Lecter Specters—serial killer ghosts—calm and happy which means they'll revert to being killers able to manifest. They could end up with many serial-killer ghosts like the Nightmare rampaging around Chicago killing. They need to rescue Lindquist. Dresden considers that if Kravos had access to his magic as a Ghost that it stands to reason that he should as well.
In Cold Days, the Summer Lady, Lily, implied that the Contagion—later named Nemesis—corrupted Harry Dresden's first three big cases: Victor Sells, Phillip Denton and his Hexenwolves, and the Nightmare.