One could say that the quantitative study of earthquake source dynamics began with the development of reliable seismographsSeismograph at the end of the nineteenth century. Understanding of earthquake source dynamics has been deepened by the densification of observation networks, the diversification of observation methods, the sophistication of data analysis, the development of sophisticated mathematical models, and the advent of large-capacity, high-speed computers. This chapter provides an overview of the historical process of developing a deeper understanding of earthquake ruptures and the current state-of-the-art. As will be discussed at the end of this chapter, seismic activity observations suggest the presence of intense nonlinearities in earthquake ruptures, which may shape the nature of earthquake ruptures. Some chapters in this book discuss the origin of nonlinearities and the effects of nonlinearities on earthquake ruptures. Such nonlinearities, in fact, manifest themselves in many aspects of earthquake rupture phenomena. Some later chapters discuss the origins of nonlinearities and their effects on earthquake rupture.