Various anthropogenic activities result in a continuous discharge of contaminants of emerging concern (CEC) into the natural environment. The remediation of these substances is an emerging concern to safeguard life on Earth. CECs and their removal have become a growing concern, which is being investigated in different wastewater treatment processes. Therefore, a comprehensive study is required to find appropriate low-cost, eco-friendly, and efficient technology to remediate different kinds of CECs from wastewater. The partial removal of CECs, such as endocrine-disrupting compounds, pharmaceuticals, personal care products, and heavy metals have been discussed in this review. The results of the review show that the majority of the research in recent years has focused on using phase-changing processes, including adsorption in different solid matrices and membrane processes, followed by biological treatment and advanced oxidation processes. This paper focuses on the type of CEC being removed, the conditions of the process, and the outcomes achieved. The main trends in the field are also highlighted along with perceptive comments and recommendations for further developments, as well as the identification of the current knowledge gaps and future research directions related to the application of these technologies for water treatment and restoration.