Their first major cartoon character, Koko the Clown, was a product of rotoscoping. In 1929 they changed the studio name to Fleischer Studios. It was also around this time that the studio started to experiment with sound. Talkartoons became a hit with the studio going into the early 30's with their character Betty Boop eventually becoming the star and getting her own show which ran until 1939.
Fleischer Studios had their biggest hit when they licensed E.G. Seger's comic character Popeye starting in 1933. Popeye even surpassed Micky Mouse in popularity at the time. The studio was hitting its stride by 1936, and this made their parent company, Paramount, demand more output in shorter amounts of time. This led to the first ever strike in the motion picture industry. The strike lasted five months and resulted in Fleischer cartoons being boycotted throughout the strike's duration. Max Fleischer had been bugging Paramount to let them do a full length animated film, but they didn't go for it until Disney pulled it off with Snow White and the Seven Dwarfs. Once Disney had proven that it could be done and people would go see it (and see it they did, Snow White still tops box office returns when adjusted for inflation for animated films), Paramount then demanded a movie be done by Christmas 1939.
Things were going downhill quickly for the Fleischer brothers. The move to Miami and the stress of trying to get Gulliver's Travels made had damaged their relationship. They eventually stopped talking to one another after Max slept with Dave's receptionist. Dave eventually gained full control of production, with Max dealing with business affairs and research. Things didn't go much better with Dave picking what to make. Their new cartoons were very unpopular, with only Popeye sticking out as a money-maker. Max attempted to save the studio by acquiring the rights to Superman, which was a very popular character, but was too little too late. Superman was also expensive to product. Their first short featuring Superman cost $50,000, the highest of any short of that time.
Fleischer Studios still hadn't paid Paramount all their penalties and Paramount eventually fully acquired them, though letting them keep producing cartoons. They hoped that Popeye, Superman, and the studio's second film could get things going again. Mr. Bug Goes to Town, the studio's second feature, was not going to save them. It was first previewed on December 5th, 1941. Critics enjoyed it, but theater owners rejected it. Two days later, Pearl Harbor was bombed by the Japanese and Paramount canceled the release of the film until February. Paramount had had enough of the Fleischer brothers and had made them sign resignation forms ahead of the films release to be used at the company's discretion. Dave quit, and Max was fired shortly after. Mr. Bug Goes to Town, originally titled Hoppity Goes to Town, was a complete bomb, and that, together with Paramount noticing that both of Disney's recent releases, Pinocchio and Fantasia tanked at the box office too, led Paramount to completely abandon making animated films. Fleischer Studios was renamed Famous Studios in 1942.
Fleischer Studios still exists today, but not as a traditional studio. Max's grandson, Mark Fleischer, currently owns the studio, which owns the rights to Betty Boop, Koko the Clown, Bimbo, and Grampy. Mark basically controls merchandising on these characters. I'm guessing Betty Boop is the only one making anyting. Superman was eventually bought by Warner Bros., and Popeye's cartoons are owned by Turner Entertainment.