Repetition is an integral part of nature. Hardly can we go by our daily lives without encountering repetitive structures or activities. Being such a ubiquitous and fundamental phenomenon, natural repetition has been an important subject of study in a variety of science and engineering disciplines. In a sense, computer science existed primarily for dealing with repetitive computations. However, most prior methods can handle only artificial repetitions which may lack proper variations commonly see in nature. Thus, one of my main research directions is to design general and fundamental algorithms that can compute natural repetitions within a variety of application contexts. This endeavor can not only help us understand how the nature works but also build better and more powerful computational tools, involving knowledge from and applications to different fields such as computer graphics/vision, multi-media, image/video processing, sampling theory, and parallel computing.