Visualizations that adopt a first-person point of view allow observation and, in the case of interactive simulations, experimentation with relativistic scenes. This paper gives examples of three types of first-person visualizations: watching objects that move at nearly the speed of light, being a high-speed observer looking at a static environment and having a look-around near a compact object. I illustrate and explain the main aspects of the visual observations, outline their use in teaching relativity and report on teaching experiences. For teaching purposes, our visualization work is available on the website www.spacetimetravel.org and its German counterpart www.tempolimit-lichtgeschwindigkeit.de. This paper assumes some basic knowledge about relativity on the part of the reader. It addresses instructors of physics at the undergraduate and advanced secondary school level as well as their students. (Contains 9 figures and 3 footnotes.)