Nuclear magnetic resonance (NMR) is a sophisticated technology to gain insights into the Earth's physical and chemical properties, such as porosity, permeability, fluid viscosity, and pore structure in near-surface environments. The signal-to-noise ratio (SNR) is one of the most critical challenges in applying NMR to reservoir pore media, as the data acquired from NMR instruments must be inverted into NMR relaxation spectrum to estimate formation information, where the inversion is an inherently ill-posed problem. In particular, the target of NMR detection is transitioning to the ultra-deep reservoirs, which are characterized by an extremely low porosity. In these environments, the NMR data typically exhibit very low SNR due to the limited fluid volume within the sensitive region and harsh measurement conditions, both of which significantly impact the quality of the inverted spectra. Therefore, enhancing SNR prior to spectrum inversion, i.e., through data denoising, is essential. This paper reviews methods for denoising NMR echo data, including mathematical transformation methods, morphological filtering techniques, and artificial intelligence (AI)-based methods. Their advantages and disadvantages of each method were compared and analyzed. The development trend in NMR data denoising is summarized. A multi-dimensional denoising strategy that integrates mathematical transformation and AI technologies, along with the development of lightweight AI models, shows great promise for NMR echo data denoising.