Adsorption is a widely used technology for removing and separating heavy metal from water, attributed to its eco-friendly, cost-effective, and high efficiency. Adsorption isotherm modeling has been used for many years to predict the adsorption equilibrium mechanism, adsorption capacity, and the inherent characteristics of the adsorption process, all of which are substantial in evaluating the performance of adsorbents. This review summarizes the development history, fundamental characteristics, and mathematical derivations of various isotherm models, along with their applicable conditions and application scenarios in heavy metal adsorption. The latest progress in applying isotherm models with a one-parameter, two-parameter, and three-parameter in heavy metal adsorption using carbon-based materials, which has gained much attention in recent years as low-cost adsorbents, is critically reviewed and discussed. Several experimental factors affecting the adsorption equilibrium, such as solution pH, temperature, ionic strength, adsorbent dose, and initial heavy metal concentration, are briefly discussed. The criteria for selecting the optimum isotherm for heavy metal adsorption are proposed by comparing various adsorption models and analyzing mathematical error functions. Finally, the relative performance of different isotherm models for heavy metal adsorption is compared, and the future research gaps are identified.