Computer-aided exploration and visualization can be important to both progress and appreciation of mathematics. This principle can be applied either in conducting research, or in communicating it to students—-or while engaging students in expository or exploratory projects. First, I will share some results and illustrations from my own research on the geometry and dynamics of higher-dimensional continued fractions, some resulting from collaboration with students. Second, I will talk about the paradigm of Experimental Geometry Labs (or Experimental Mathematics Labs) that is being used at many universities, both in the US and abroad, to provide students with meaningful early access to mathematical research.