In this paper, we survey Vietnamese automatic speech recognition (ASR). The objective of this survey is to provide an overview of the current status and remaining challenges of implementing a Vietnamese ASR. Recently, there are some studies on ASR for Vietnamese language; however, these studies encounter some obstacles and the results obtained compared to other languages such as English or Mandarin are lower. With regards to Vietnamese speech recognition, we will examine the methods of building a system along with speech data and text data collection techniques and available speech resources. We review both the methods applied to acoustic modeling and those used to language modeling. In addition, we convey some directions for future research.