Predicting the time rate of consolidation is one of the major aspects of structure design, founded on compressible fine-grained soil. The time to achieve the required advancement of the consolidation process is proportional to the coefficient of consolidation (cv). In practical applications, the settlement rate is directly related to the excess pore water pressure dissipation rate. A plethora of interpretation methods have been proposed for determining consolidation parameters from laboratory one-dimensional consolidation test in the past decades. This state-of-the-art review presents a comprehensive literature study of available approaches for establishing both coefficient of consolidation and end of primary (EOP) consolidation using compression and pore water pressure laboratory data. The classification of the methods has been made to set in order interpretation approaches for future selection and comparisons. The first part of the paper describes approaches based on graphical curve-fitting. This part includes five approaches: square root of time fitting approach, Semi-logarithmic fitting approach, Differential methods, Hyperbolic approach, and approach based on excess pore water pressure dissipation. In addition, a method comparison study has been performed to evaluate the degree of agreement between selected methods statistically. For this purpose, simple regression and Bland & Altman differences analysis have been used. The second part refers to the computational-based approach, covering a wide range of methods centred on full-matching treated by least-squares, correlational equations linking cv with index properties and soft computing approaches. A thorough insight into recently published literature on machine learning and physics-informed deep learning incorporated to derive the representative value of cv has also been compiled.