Estimated numbers of scientific journals in print each year are approximately close to 70,000-80,000 (Rowland, McKnight, & Meadows, 1995). Institute of Scientific Information (ISI) each year adds over 1.3 million new articles and more than 30 million new citations to its science citation databases of 8,500 research journals. The widely available electronic repositories of scientific publications, such as digital libraries, preprint archives, and Web-based citation indexing services, have considerably improved the way articles are being accessed. However, it has become increasingly difficult to see the big picture of science. Scientific frontiers and longer-term developments of scientific disciplines have been traditionally studied from sociological and philosophical perspectives (Kuhn, 1962; Stewart, 1990). The scientometrics community has developed quantitative approaches to the study of science. In this article, we introduce the history and the state of the art associated with the ambitious quest for detecting and tracking the advances of scientific frontiers through quantitative and computational approaches. We first introduce the background of the subject and major developments. We then highlight the key challenges and illustrate the underlying principles with an example.