The slowness information of near-wellbore formation is of great significance to oil-gas exploration and development, which can reflect the properties of rock. However, the near-wellbore formation presents radial heterogeneity with a variable slowness profile, due to the effects from mud filtrate invasion, wellbore stress, drilling machinery damage and fracturing operation. Accordingly, extracting radial slowness profile from acoustic logging inversion has important application value in identifying invasion depth, evaluating wellbore stability, guiding well completion design, and evaluating fracturing effect. Therefore, we have investigated the current inversion methods constructed by researchers in this paper and divided them into three categories: the inversion with arrival time of waves, the inversion with slowness-time coherence (STC), and the inversion with wave dispersion. After comprehensive research and analysis, we found that the usability and performance of the methods is different due to the difference of target mode waves and their algorithms. Based on the obversions, we further concluded the advances of the methods in extracting the slowness profile near a wellbore from array acoustic logging data, and compared their performances in real applications.