Arguably the greatest work of Ivan Turgenev, a major Russian writer of the mid- to late 19th century. It was first published in 1862, and the resulting furor over it caused Turgenev to leave Russia, only returning a few times for brief visits. Its subject is the ideological conflict between the young revolutionary nihilists (the "sons") and the older generation of citizens who accept reform to a point, but are nonetheless czarists (the "fathers").
It should be noted that a "nihilist" in this context does not mean someone who "believes in nothing". The Russian conception of nihilism, at least at the time, was the belief that all the old institutions should be destroyed and replaced with new institutions based somewhat on democratic ideas. In Fathers and Sons, this is taken to what we might consider an extreme; the main character, Bazarov, goes so far as to claim that love is not real, that a better conception of emotion will replace it.
Bazarov is the center of the novel. A doctor by trade, he embodies the spirit of the revolution; casting aside wealth, tradition, religion, social mores, and nearly everything else as a product of the Czar's autocracy. He and Arkady, his protégé, travel to the latter's home in a pseudo-feudal town whose 'lord' is Arkady's father, Nikolai Petrovitch. This is the basis for most of the rest of the novel, as much of it consists of conflicts between Bazarov and Arkady on the one hand and Nikolai and his brother Pavel on the other.
There is some debate over which side Turgenev favored; as far as I know, there's no real scholarly consensus on it. Regardless, both Russian conservatives and radicals at the time attacked Turgenev for his portrayal of Bazarov; the conservatives felt he was made too much of a virtuous protagonist, the radicals thought he was presented as something of a caricature. Heavy criticism on both sides was largely responsible for his self-imposed exile from Russia. Nonetheless, Fathers and Sons is today recognized as one of the great works of Russian literature.