The painting was part of the neoclassical style, popular in the 1780s, that depicted subjects from the Classical age, in this case the story of the execution of Socrates as told by Plato in his Phaedo.

[1] In this story, Socrates has been convicted of corrupting the youth of Athens and introducing strange gods, and has been sentenced to die by drinking poison hemlock.

In the painting, an elderly Socrates is dressed in a white robe and sits upright on a bed, one hand extended over a cup, the other gesturing in the air; he is still teaching.

On the stairway in the background, Socrates' wife Xanthippe, who had been dismissed earlier by her husband, takes a wistful glance backward at the scene.

[5] David signed this painting in two places; he put his full signature under Crito, the young man clutching Socrates's thigh, and his initials under Plato.

[8] More generally, Socrates was a popular subject at the time as an example of Enlightenment values: a man who kept to the truth with admirable rationality and self-control.

The two had something of a rivalry before, with both hoping to become Director of the French Academy in Rome when the position next opened; the critics felt the two paintings decisively settled the matter in favor of David.

Count Potocki derisively stated that Peyron's work "has shown up the quality of David's picture by proving to the public how far beneath him one could be".

The English painter Joshua Reynolds wrote that The Death of Socrates was "the greatest work of art since the Sistine Chapel and Raphael's Stanze in the Vatican.

[2] The painting was sufficiently successful that David showed it again at the Salon of 1791; it still attracted interest due to the changed political environment, as heroic stories from an earlier age fit the mood of the early French Revolution.

[2] An 1826 exhibition intended to raise money for the Greek War of Independence displayed much of David's work at the Galerie Lebrun, including The Death of Socrates.

The exhibition attracted much interest due to a backlash from the post-Bourbon Restoration royalist government, which disliked David and had refused permission for his body to be buried in France, albeit more for his Revolutionary-era paintings than Socrates.