Prediction of scouring characteristics is one of the major issues in hydraulic and hydrology engineering. Over the past five decades, numerous empirical formulations (EFs), based on the regression of scouring data observed from laboratory experiments in the field, have been developed to predict scouring characteristics (typically, the equilibrium scour depth); yet, these EFs are sensitive to uncertainty of effective parameters and in some cases could not comprehend the actual internal mechanism between variables. In the last 20 years, Soft Computing (SC) approaches have been increasingly adopted as an alternative for modeling scouring depth surrounding hydraulic structures. In this respect, several SC algorithms are examined as new era of modeling methodologies for extracting scouring depth equations. Lately, these algorithms have been vastly adopted for scouring simulation with various advanced version of SC such as hybrid intelligence models. The motivation of the current research is to exhibit all the established researches on the implementation of EF and SC models for multiple scouring depth modeling such as around pipeline, bridges abutment, piles and grade-control structures. A comprehensive review of the up-to-date researches on the scouring depth phenomena is presented, placing special emphasis on the recent applications of SC models and also recalling all the performed experimental laboratory studies. The review is included an informative evaluation and assessment of the surveyed researches. The improvement in prediction performance provided by the SC models when compared to empirical formulations is discussed and based on the current state-of-the-art, several research gaps are recognized, and possible future research directions are proposed.