Computational Geometry has been a thriving research area for the past 20 years. During that time, the field has grown from a handful of researchers working on a small set of problems to a full-blown research area with multiple conferences and journals and many hundreds of researchers. The initial motivation for the field was to develop algorithms that would find application in practice in other fields. In this talk, I will trace some of the original history of the field to see where it came from. Next, I demonstrate some application areas where computational geometry has been applied. These applications are largely drawn from computer graphics and visualization. Techniques that apply to sampling problems as well as progressive refinements of meshes will be shown. In addition, algorithms for graph layout will be considered. These applications will be presented as case studies. Some begin with a problem for which solution techniques need to be developed. Others begin with a technique and problems are found to which the technique applies. In each case, there is an underlying implementation that justifies the work. Difficulties of the implementation will also be discussed.