A league system is a hierarchy of leagues in a sport that teams can be promoted or relegated between, depending on finishing positions or playoffs. They are often called pyramids due to their tendency to have more (regional) divisions at the bottom.

Wikipedia has articles on the following league systems:

Association Football (Soccer)

• Belgian football league system
• Italian football league system
• Swedish football league system
• United Kingdom
  • English football league system
  • Northern Irish football league system
  • Scottish football league system
  • Welsh football league system
• United States soccer league system

Tennis

• Davis Cup structure