The following facts, or empirical regularities, about yield curves are well-known:
See, for example, Money & Banking textbooks by Cecchetti and Schoenholtz or Mishkin for more information.
The video below is an animation of every US Treasury bond yield curve from January 4, 1965 through the present. Watch the video to see if you can connect each fact with the behavior of the actual yield curve.
The data for the animation were obtained from Federal Reserve Economic Data (FRED).The Python code that I used to create this animation is available in this Github repository.