Clustering is an effective tool for astronomical spectral analysis to mine clustering patterns among data. With the implementation of large sky surveys, many clustering methods have been applied to effectively and automatically tackle spectroscopic and photometric data. Meanwhile, the performance of clustering methods under different data characteristics varies greatly. Aiming to summarize the astronomical spectral clustering algorithms and lay the foundation for further research, this paper gives a review of clustering methods on astronomical spectra data including next three parts. Firstly, lots of clustering methods on astronomical spectra are investigated and theoretically analysed appearing in algorithmic ideas, applications and features. Secondly, experiments are carried out on the unified datasets constructed by three criteria (spectra data type, spectra quality and data volume) to compare the performance of typical algorithms and the spectra data are selected from LAMOST and SDSS surveys. Finally, source codes of the comparison clustering algorithms and manuals for usage and improvement are provided on https://www.github.com/shichenhui/SpectraClustering.