Thermal plumes have been the subject of research due to their technological and environmental importance in many physical processes, such as spread of smoke and toxic gases from fires, and release of gases from volcanic eruptions and industrial stacks. In this paper, history and current trends in the computation of turbulent buoyant plume have been reviewed. First an introduction to the turbulent buoyant plume is presented, which includes its importance, the flow physics, and heat transfer characteristics. Subsequently, a brief review of the experimental works reported in the literature is presented, followed by a review of the computational methods. Several subgrid-scale models used in large eddy simulation performed in the literature to simulate buoyant plume are discussed. Further, the boundary conditions, computational schemes, and computational grid sizes are discussed. The efficacy of various Reynolds-averaged Navier-Stokes (RANS)-based modeling techniques to simulate turbulent buoyant plumes has been reviewed. It has been concluded that the dynamic subgrid-scale models perform fairly well in predicting the statistics of turbulent buoyant plume. However, no subgrid-scale model has been able to capture the inverse energy cascade, called backscatter, which is an important phenomenon in the evolution of a plume. In case of RANS modeling of plumes, models based on the generalized gradient diffusion hypothesis capture the flow accurately as compared with the models based on the simple gradient diffusion hypothesis.