The suitors are the nobles of Ithaca and the neighboring islands who court Penelope while Odysseus is away. They are sons of the most important men of the region, and among them Antinous and Eurymachus stand out and lead the group, along with Amphinomus, who is well regarded by Penelope.
The problem they create is concrete. They install themselves in Odysseus's palace, slaughter the oxen, sheep, and goats of the flock, drink the house's wine, and sleep with the maidservants. Telemachus says in the assembly that they avoid the house of Icarius, Penelope's father, who would be the one to fix the gifts and give his daughter to whomever she chose, and prefer to spend the day at his house. The custom, Penelope herself recalls, is that suitors bring oxen and sheep to the feast and give gifts, and that they "do not devour another's livelihood without payment."
They stay because the situation favors them. Penelope does not refuse marriage, but postpones it; Telemachus, still young, lacks the strength to drive them out and cannot send his mother away against her will, under penalty of paying Icarius and facing the censure of men and the Erinyes; and the people, in the assembly, are moved and stay silent. When Telemachus sets out for Pylos and Sparta, Antinous and the others set an ambush to kill him on his return. Later, Eurymachus says that Antinous, in truth, wanted to reign over Ithaca.
The poem judges the group by how they behave toward strangers. Antinous throws a footstool at the beggar who asks for alms, and Odysseus replies, without losing composure, that if there are gods and Erinyes of beggars, death will reach Antinous before the marriage. When Odysseus finally speaks, he will say that they devastated the house "without fearing the gods" nor the vengeance of men. The contest of the bow and the slaughter in Book XXII close the story of the suitors; their kin, in the last book, are the ones who try to avenge them.