Based on the features of nonionization, noninvasiveness, high penetration, high resolution, and spectral fingerprinting of terahertz (THz) waves, terahertz spectroscopy has great potential in the biomedical field. Based on terahertz spectroscopy, combined with different analysis algorithms, different research groups have achieved qualitative and quantitative identification of mixture samples. However, actual biological mixture samples often comprise different components, including water, which results in poor spectral signal-to-noise ratio and large errors in the final spectral analysis results. For these problems, the use of noise reduction and reconstruction algorithms is effective solutions. These algorithms improve the signal-to-noise ratio of the spectrum by eliminating invalid information in the spectral data or extracting valid information. Finally, these algorithms can be combined with analysis algorithms to provide high-precision qualitative and quantitative identification of biological samples. In this paper, we discuss the main algorithms applied in terahertz spectroscopy over the past five years and summarize their advantages and disadvantages.