Kraven, real name Sergei Kravinoff, was a big game hunter known for his physical prowess. In 1963's The Amazing Spider-Man #15 Kraven begins hunting Spider-Man to prove himself the greatest hunter in the world. Kraven uses his bare hands in combat and is a formidable foe for Spider-Man... even before he takes a serum that gives him super strength.
Kraven is bested a few times in battle and gives up his hunt. Calypso Ezili, Kraven's lover, convinces him that Spider-Man released his animals from their cages. Kraven resumes his hunt for Spider-Man. The two meet in battle but, unknown to Kraven, Calypso shot Spider-Man with a tranquilizer to interfere with his "spider sense" ability. Kraven realizes that something is wrong because he is winning so easily. Kraven ends the battle with Spider-Man out of honor for a fair fight.
Kraven's origin story is told through flashback in Web of Spider-Man #31 which, coincidentally, tells the story of "Kraven's Last Hunt". Kraven, sensing that his abilities are fading, feels a need to prove that he is a master hunter once and for all. He finds Spider-Man, defeats him in a fight, and shoots him in the head with a tranquilizer. Kraven then buries Peter Parker alive.
Kraven dons the Spider-Man costume and defeats the villain known as Vermin. This is significant because, in previous books, Vermin was only able to be defeated by a team up between Spider-Man and Captain America. In Web of Spider-Man #31 Kraven proves himself the better fighter, the more ruthless character, and the better Spider-Man.