Emerging pollutants (EPs) are the contaminants of concern in water systems. These are mainly due to anthropogenic activities and are not always removed during water treatment, eventually affecting the quality of water supply systems (WSSs). These pollutants vary from organic pollutants such as pharmaceuticals, pesticides, and flame retardants to inorganic pollutants like heavy metals or illicit drugs. Currently, there is a lack of adequate research on the chronic health effects of these pollutants. In addition, climate change plays a role in immobilizing these pollutants. Consequently, considering the increasing effects visible in many countries, the rising levels of contaminants have strained the effectiveness of water treatment facilities. As water supply is an essential service to communities, it is necessary to ensure the reliability against risks of EPs. Therefore, it is important to protect the health and safety of consumers. Climate change has brought threats to water infrastructures, like many others. This review examined the effect of climate change on EPs in water supplies by providing a detailed review of the contaminants, evaluating their potential toxicity, and determining the appropriate water treatment technologies. The role of the WSS in EP immobilization was examined in addition to the potential effect of climate change. This review of different critical and relevant literature aids with the identification of current research gaps. Based on the identified gaps, a research framework was developed for the future investigation of EPs.