With the recent developments of technology and the advances in artificial intelligence and machine learning techniques, it has become possible for the robot to understand and respond to voice as part of Human-Robot Interaction (HRI). The voice-based interface robot can recognize the speech information from humans so that it will be able to interact more naturally with its human counterpart in different environments. In this work, a review of the voice-based interface for HRI systems has been presented. The review focuses on voice-based perception in HRI systems from three facets, which are: feature extraction, dimensionality reduction, and semantic understanding. For feature extraction, numerous types of features have been reviewed in various domains, such as time, frequency, cepstral (i.e. implementing the inverse Fourier transform for the signal spectrum logarithm), and deep domains. For dimensionality reduction, subspace learning can be used to eliminate the redundancies of high-dimensional features by further processing extracted features to reflect their semantic information better. For semantic understanding, the aim is to infer from the extracted features the objects or human behaviors. Numerous types of semantic understanding have been reviewed, such as speech recognition, speaker recognition, speaker gender detection, speaker gender and age estimation, and speaker localization. Finally, some of the existing voice-based interface issues and recommendations for future works have been outlined.