As of 2015, facts about Jesus' brothers include their names -- James, Joses, Judas and Simon. Jesus left James in charge of his followers. Judas' children were named Zechariah and James. These statements are among the few found in the Bible and other texts that historians and theologians consider accurate.
There is still much debate about Jesus' nuclear family, due to the multiple interpretations not only of the linguistic nature, but of culture and traditions of the time as well. A popular example is that many believe that Jesus' brothers were instead step- or half-brothers or possibly even cousins because of the tradition of Levirate marriage. Mary was believed to have out-lived Joseph.