Short answers, pulled from the story.
Pope Julius II commissioned Raphael to decorate the Stanza della Segnatura in 1509. The artist worked on this massive fresco project until 1511 within the Apostolic Palace in Vatican City.
Plato stands on the left side holding a copy of Timaeus while arguing for timelessness through abstract forms. Aristotle occupies the right position carrying Nicomachean Ethics and looks into the physicality of life and the visible world.
Raphael included a self-portrait beside Ptolemy among the ancient philosophers gathered in the painted scene. Leonardo da Vinci is believed to be portrayed through Plato's aged features and Michelangelo appears as Heraclitus with varicose veins visible in his legs.
A study for Diogenes exists in the Städel Museum in Frankfurt while another group around Pythagoras is preserved in Vienna's Albertina Museum. Copies also exist in Königsberg Cathedral, the University of North Carolina at Asheville, and Baylor University's Brooks College seminar room.
The building takes the shape of a Greek cross which some suggest shows harmony between pagan philosophy and Christian theology. The architecture was inspired by the work of Bramante who helped Raphael with the architectural elements in the picture.