Robert M. Grant writes (The Anchor Bible Dictionary, v. 3, p. 1133):
Justin’s first work seems to have been his treatise Against all Heresies [now lost] . . . Later he composed his Apology now divided into two parts. The work is addressed to Antoninus Pius and his two adopted sons. Its date may be given by Justin’s insistence on eternal fire for the wicked, for in the year 156 Polycarp of Smyrna, favorably received at Rome the year before, was burned alive after threatening his judge with “eternal fire.” Justin’s essay begins with the demand to investigate accusations and explains what Christians believe and do. The so-called “second apology” looks like a continuation of the first, perhaps with more emphasis on the philosophy espoused by the future emperor Marcus Aurelius.
Justin Martyr was a second century Christian apologist. His apology is dedicated to Emperor Antoninus, who ruled from 138-161. His apology may be dated internally from the statement in chapter 6 that “Christ was born one hundred and fifty years ago under Cyrenius.” Since Quirinius entered office in the year 6 C.E. according to Josephus, the apology may be dated to the year 156 CE.
His three works are known as the First Apology, the Second Apology, and the Dialogue with Trypho. Irenaeus tells us that Justin Martyr wrote a work against Marcion, which is now lost. Some authentic materials are preserved in the fragments of Justin quoted by other writers, although some of these fragments may be suspect.
The other documents attributed to Justin Martyr listed above – the Hortatory Address to the Greeks, On the Sole Government of God, and On the Resurrection – are of dubious authenticity. They may have been written instead by another Christian author, now unknown. It has been suggested that the Discourse to the Greeks was originally a Jewish treatise.
Justin Martyr (d c 165 CE) was a Christian Apologist and Martyr. He was born around the turn of the century in modern day Palestine. He claimed to have been raised a Gentile, and in his search for truth he studied with the Stoics, Aristotelians, Pythagoreans, and Platonists. Impressed by the devotion of Christian martyrs, he was eventually converted to Christianity by an old Christian who taught him about the Hebrew prophets. According to Justin, Christianity filled the highest aspirations of Platonic philosophy and was, therefore, the “true philosophy.” During the reign of Antoninus Pius (131-161) he taught in Rome, influencing Tatian and Irenaeus. He was one of the first to consistently use Greek philosophy (especially Platonism) to explain Christian doctrine, thereby setting himself in dramatic opposition to Tertullian, who would ask “what does Athens have to do with Jerusalem?” The Logos (God immanent), he believed, was “other than” the Father (God transcendent) in number, but not in will. Three of his writings, The First Apology, The Second Apology, and The Dialogue with Trypho, the Jew, exist in complete form, though there is some question about the precise relationship between the First and Second Apology. Justin, a central figure in the history of second century Christian thought, suffered martyrdom early in the reign of Marcus Aurelius under Junius Rusticus (prefect 162-168).
http://www.ntcanon.org/Justin_Martyr.shtml