In this post, I want to give a short overview of the development of various schools of chess in a chronological order. Note that I am not an expert on that topic. I have just read a lot and want to write it down on my blog instead of my notebook.
Romantic chess was the style of chess that was played up to around 1880. It was similar to the romantic era in the arts. Emotional expression was favored instead of playing good. People in that era sucked at chess. They played mostly 1.e4 and the game consisted of rapid tactical maneuvers instead of slow development of the pieces. Gambits had to be accepted as everything else was cowardly. Paul Morphy is a famous player from that era.
Romantic Chess was superseded by the modern school of chess. This was mainly due to Steinitz who introduced modern elements such as positional play, closed positions the importance of controlling the center, as well as the importance of space. Another important chess theorist of that school is Tarrasch. This is basically how most of chess is still played today.
Later, the modern school of chess was superseded by the hypermodern school. While in modern chess, players try to control the center as pieces in the center are more flexible, in hypermodern chess the players control the center via the flanks. This can be achieved by fianchettoing their bishops. The center is then slowly undermined. Common hypermodern openings are all of the Indian Defenses. One train of thought that to me defines the hypermodern school the ideas introduced by Tarrasch being too rigid and dogmatic to encompass technically good chess. The most famous hypermodern player is Nimzowitch