Short answers, pulled from the story.
The School of Athens was painted between 1509 and 1511. Raphael created it as part of a commission from Pope Julius II to decorate the rooms now called the Stanze di Raffaello in the Apostolic Palace in Vatican City.
The two central figures are Plato, on the left, and his student Aristotle, on the right. They stand at the architectural vanishing point of the fresco; Plato holds the Timaeus and Aristotle holds the Nicomachean Ethics.
Leonardo da Vinci is believed to be portrayed through the figure of Plato at the center of the fresco. Michelangelo is similarly believed to appear as Heraclitus, the figure slumped alone on the steps.
The original fresco is in the Apostolic Palace in Vatican City, in the room known as the Stanza della Segnatura. The Victoria and Albert Museum in London holds an 18th-century copy on canvas, dated 1755 and attributed to Anton Raphael Mengs.
The overhead tondo above the fresco bears the Latin phrase "Causarum Cognitio", meaning knowledge of causes. This echoes Aristotle's argument in his Metaphysics that wisdom consists in knowing why things happen, not merely that they do.
The full cartoon for The School of Athens is held at the Pinacoteca Ambrosiana in Milan. It is missing the architectural background and the figures of Heraclitus, Raphael himself, and Protogenes, which were apparently resolved after the main figure compositions were established.