Sergei Eisenstein's montage theory
Illustrations from Battleship Potemkin (1925) and
The Man with the Movie Camera (1929)

The Russian Soviet filmmaker Sergei Eisenstein believed that montage (juxtaposing images by film editing) could create ideas or have an impact not found in the individual images. Two or more images together create a "tertium quid" (third thing) that makes the whole greater than the sum of its individual images. Here are two sets of images from the end of the "Odessa Steps" sequence of Battleship Potemkin. The three still shots of stone cherubs, when edited together rapidly, give the impression of throwing a punch. Similarly, the three stone lions, seen in rapid succession, suggest being aroused from slumber to anger. For Eisenstein, the kind of montage illustrated in Battleship Potemkin could function to raise political awareness and militancy.

The images below are from Vertov's Man with a Movie Camera. The first pair is an example of graphic match: two images unnrelated except for visual similarity. The second and third pairs are examples of using montage for thematic contrasts.
In the two examples below. Vertov uses montage to make a political point. He edits together shots of women in beauty parlors with shots of women doing productive work (in a factory in the first pair of images, and as a film editor in the second pair). This montage supports Vertov's political theme, calling for productive labor and an end to activities that the filmmakers considered to be frivolous.
See also match cuts for a related form of montage.