Both digital fountain codes and network coding are efficient technologies for improving transmission efficiency of the networks. Network fountain codes, which are the combination of these two technologies, are of great importance in both theories and applications. In this paper, the development of digital fountain codes and network fountain codes are overviewed. Firstly, the recent research progress of digital fountain codes is surveyed, and the researches of some typical types of digital fountain codes are introduced. Secondly, the current researches on network fountain codes are summarized. The related theories and the latest research achievements of homogeneous network fountain codes, heterogeneous network fountain codes and wireless network fountain codes are introduced, while the existing problems of current researches are discussed. Finally, the development trend of network fountain codes concerning both theories and applications are analyzed and expected.