Considerable attention has been devoted in the past in modelling the initial dilution of the ocean discharge of wastewater. Asymptotic approaches have commonly been used in developing empirical initial dilution models with the aid of dimensional analysis and laboratory or field data. This paper elaborates problems associated with the use of the asymptotic approach in modelling initial dilution of buoyant jet discharges in moving waters. Critical reviews of basic concepts of the approach and numerical evaluation of the reliability of its solutions are presented in this study. Alternative approaches to modelling initial dilution using Artificial Neural Networks (ANN) and Response Surface Methodology (RSM) are also discussed. The paper also identifies potential research areas to modelling initial dilution based on, not only physical judgement, but also statistical evaluations.