The traditional cultures of Aboriginal Australians include a significant astronomical component, perpetuated through oral tradition, ceremony, and art. This astronomical knowledge includes a deep understanding of the motion of objects in the sky, which was used for practical purposes such as constructing calendars and for navigation. There is also evidence that traditional Aboriginal Australians made careful records and measurements of cyclical phenomena, recorded unexpected phenomena such as eclipses and meteorite impacts, and could determine the cardinal points to an accuracy of a few degrees. Putative explanations of celestial phenomena appear throughout the oral record, suggesting traditional Aboriginal Australians sought to understand the natural world around them, in the same way as modern scientists, but within their own cultural context. There is also a growing body of evidence for sophisticated navigational skills, including the use of astronomically based songlines. Songlines are effectively oral maps of the landscape, and are an efficient way of transmitting oral navigational skills in cultures that do not have a written language. The study of Aboriginal astronomy has had an impact extending beyond mere academic curiosity, facilitating cross-cultural understanding, demonstrating the intimate links between science and culture, and helping students to engage with science.