Master Roshi lives on an island with a house built on it, known as Kame House. Master Roshi is often referred to as The Turtle Hermit, due to the heavy turtle shell that he and his students wear on their backs for weight training. He used to be the strongest fighter on Earth, however his power level pales in comparison to any of the Z Fighters.
He was Goku's and Krillin's original Martial Arts instructor. He put them through tough training, until they were able to participate in their first World Martial Arts Tournament during the original Dragon Ball series. In the tournament Master Roshi had to enter it himself under an alter ego, in order to make sure that his students did not win it, so that they would still have a challenge and would not become disillusioned. He barely won against Goku in the final match.
Master Roshi is very old, and has apparently drunken from the fountain of youth (information obtained from the dubbed version of the original Dragon Ball series). He has a very dirty mind and is constantly watching young girls on TV in his spare time, or looking at dirty magazines. He even bribes the young teen Bulma, to lift her dress for him in exchange for a Dragonball, in the Dragon Ball timeframe.
Master Roshi is the inventor of the Kamehameha Wave attack. It took him 50 years to master the Kamehameha, while Goku only had to watch Master Roshi perform the attack one time before he could pull off a basic version of it, which he later quickly mastered. Master Roshi also has the ability to increase his body size several fold, transforming himself from a frail looking old man, into something which resembles The Incredible Hulk (just the size). He does this a few times at various stages in the series, but he is still relatively weak in the form.