In this presentation, I will briefly introduce the concept of high throughput docking (HTD) and how it is used in pharmaceutical and biotech industries. A successful HTD requires not only accurate description of molecular interactions, but also efficient numerical algorithms. A couple of computational methods that we have developed for docking will be discussed. They demonstrate how this practical problem can greatly benefit from relatively simple mathematical methods. I will also discuss some challenges ahead for further improving HTD and general high throughput virtual screening.