Short answers, pulled from the story.
Thorondor, the greatest of all the birds among the Eagles in Middle-earth, had a wingspan of 30 fathoms. He ruled as the Lord of the Eagles and led them in the defense of Gondolin and in the War of Wrath.
The Eagles, or Great Eagles, in Middle-earth are immense, sapient birds that can speak and reason, standing between the fully sentient Elves and the evil Orcs. In his final notes from the late 1950s, Tolkien described them as animals taught language by the Valar but without souls, called fëar.
Gwaihir, Landroval, and Meneldor, three of the Eagles in Middle-earth, rescued Frodo Baggins and Samwise Gamgee from Mount Doom after the One Ring was destroyed. The same Eagles had earlier helped the Host of the West at the Battle of the Morannon.
Tolkien worried that the Eagles worked too well as a rescue device, calling them a dangerous machine in one of his letters and noting he had used them sparingly. He warned that a Great Eagle landing in the Shire would be absurd and would make Saruman's capture of Gandalf incredible.
Tolkien based his painting of an eagle on a crag on a work by the Scottish artist Archibald Thorburn showing an immature golden eagle. His son Christopher found that source image in Thomas Coward's 1919 book, The Birds of the British Isles and Their Eggs.
In Númenor, three of the Eagles in Middle-earth guarded the summit of the holy mountain Meneltarma, and the Númenóreans called them the Witnesses of Manwë. Another pair nested in an eyrie above the tower of the King's House in the capital, Armenelos, and many more lived around Sorontil.