<p>Full-waveform inversion (FWI) is a critical technique for deriving high-resolution velocity models in geophysical studies. However, the lack of low-frequency components in seismic data can result in significant cycle-skipping issues, leading to inaccurate inversion outcomes. Fortunately, the envelope of seismic data contains abundant low-frequency information that can be utilized to improve the inversion of large-scale background velocity models. Within the FWI framework, current envelope inversion (EI) methods can be classified into two primary categories: (1) conventional envelope inversion, which employs the waveform Fréchet derivative and is optimally suited for weak scattering scenarios, and (2) direct envelope inversion, which utilizes the envelope Fréchet derivative and demonstrates effectiveness in inverting models characterized by strong contrasts. This review paper addresses the following key aspects: (1) an overview of the principles underlying conventional envelope inversion and direct envelope inversion methodologies, alongside a detailed comparative analysis; (2) an evaluation of the limitations and effectiveness of both conventional and direct envelope inversion techniques when applied to weak and strong scattering media, supported by comprehensive numerical test cases; and (3) a thorough review of the historical development of envelope inversion, exploring its critical challenges, current solutions, and future perspectives in the field.</p>