The advancement of China’s space power strategy has been recognized to underscore the critical significance of space manufacturing. However, product quality in this field is significantly undermined by manufacturing vibrations, which are more difficult to mitigate in microgravity environments, where the vibration attenuation rate is merely 15% to 30% of that on the ground. To address this problem, a comprehensive review of techniques for vibration signal acquisition, analysis, and denoising was presented. Signal acquisition methods were classified into contact and non-contact categories, with laser Doppler vibrometry identified as a core non-contact technology that enables non-intrusive monitoring and confers unique advantages on precision manufacturing. For signal analysis, conventional time-domain and frequency-domain methods are restricted in capturing nonlinear transient features, whereas time-frequency analysis techniques (e.g., wavelet transform) can effectively characterize such complex signal properties. In terms of denoising, traditional filtering methods were often associated with the loss of critical signal details. Consequently, a shift has been made in the current mainstream strategy toward hybrid methods integrating time-frequency analysis with intelligent algorithms. Effective noise reduction for complex signals was achieved by these hybrid approaches, with their key features preserved. For instance, a signal-to-noise ratio (SNR) of 19.4 dB was achieved by the ensemble empirical mode decomposition-kernel least mean square (EEMD-KLMS) method, which represents a notable improvement over the 16.4 dB obtained by the conventional empirical mode decomposition (EMD) method. Finally, the practical engineering applications of these vibration signal processing methods were discussed, and promising future research directions were proposed.