Consolidation settlement is the time-dependent phenomenon. Coefficient of consolidation is essential to estimate the rate of settlement of structures founded on saturated fine-grained soil. One of the common methods used to determine the coefficient of consolidation is through curve-fitting procedure. These procedures involve fitting a theoretical model to experimental data obtained from laboratory tests, such as the oedometer test. The Casagrande log t method and Taylor’s root t method are the standard methods to find the vertical coefficient of consolidation (cv). To design vertical drains, Barron’s theory is commonly used which requires coefficient of radial consolidation (cr). Over the past decade, several curve-fitting procedures namely the inflection method, rectangular hyperbola method, one-point method, early-stage log t method and many more, have been developed to determine either vertical or radial coefficients of consolidation. This paper provides a comprehensive review of procedures used for computing the vertical and radial coefficient of consolidation, offering a comparative analysis with advantages, limitations, and practical use of each method. Also, cv and cr of kaolin clay are determined through various methods. This assessment will be helpful to both academics and working engineers in accurately choosing the appropriate method for estimating the rate of settlement in saturated fine-grained soils.