The single most valuable external source for James is the Jewish historian Josephus, whose Antiquities of the Jews (Book 20) reports his death. In a brief notice, Josephus describes how, after the Roman governor Festus died and before his successor Albinus arrived, the high priest Ananus seized the interval of weak authority to convene the Sanhedrin and have executed "James, the brother of Jesus who was called Christ," together with certain others, on a charge of transgressing the law; they were stoned. The date is about 62 CE.
This passage is treated by the great majority of scholars as authentic, unlike the more famous and much-disputed Testimonium Flavianum earlier in Josephus, the reference to James is generally accepted as genuine, since it is incidental, sober, and free of the Christian interpolation that marks the other passage. It matters on two counts: it independently confirms the existence of James and, through the phrase "who was called Christ," provides one of the earliest non-Christian references to Jesus as well.
Christian tradition adds a fuller and more legendary account through Hegesippus, quoted by Eusebius, which portrays James as an ascetic of extraordinary holiness, revered even by non-Christians as "the Just," and killed by being cast from the pinnacle of the Temple and clubbed, a martyrdom narrative that the atlas records as tradition rather than established fact.