Short answers, pulled from the story.
Quintus Smyrnaeus was a Greek epic poet traditionally placed in the latter part of the 4th century AD, though some scholars argue for an earlier date in the 2nd or 3rd century. He is known for his fourteen-book epic the Posthomerica, which continues the story of the Trojan War where Homer's Iliad left off. He says in book twelve of his poem that he began composing poetry in his youth while tending sheep near Smyrna, present-day Izmir.
The Posthomerica is a fourteen-book Greek epic that covers the Trojan War from the moment Homer's Iliad ends to the fall of Troy and the dispersal of the Greek fleet by storm. It narrates the deaths of Penthesileia and Memnon, the death and funeral games of Achilles, the contest between Aias and Odysseus for Achilles' armour, the building of the wooden horse, and the sack of Troy.
The Posthomerica is the earliest surviving work to cover the period between the end of Homer's Iliad and the destruction of Troy. The archaic Epic Cycle poems that Quintus drew on, including the Aethiopis and Iliupersis of Arctinus of Miletus and the Ilias Mikra of Lesches, have all been lost, making his poem the primary source for this stretch of the Trojan War story.
Cardinal Bessarion discovered the only known manuscript of the Posthomerica at Otranto in Calabria in 1450. Because the manuscript came from Calabria, the first printed edition, published by Aldus Manutius in Venice in 1504, called the poet Quintus Calabrus rather than Quintus Smyrnaeus. The familiar name was given to him by his editor Lorenz Rhodomann in 1577.
Dorotheus, a Christian poet of the 4th century known for his Greek epic The Vision of Dorotheus, has been identified as the son of Quintus Smyrnaeus. At the end of his manuscript Dorotheus identifies himself as "Dorotheus, son of Quintus the poet". Scholars support the identification because no other poet named Quintus is known from the period and Dorotheus used the same Homeric poetic structure as his father.
Quintus drew primarily on the Aethiopis and Iliupersis of Arctinus of Miletus and the Ilias Mikra of Lesches, the same cyclic poems that Virgil also used as sources. He was probably acquainted with Virgil's works. For the middle books, scholars also detect the influence of Greek tragedy, particularly Sophocles' depiction of Ajax.