Enteric viruses are common waterborne pathogens found in environmental water bodies contaminated with either raw or partially treated sewage discharge. Examples of these viruses include adenovirus, rotavirus, noroviruses, and other caliciviruses and enteroviruses like coxsackievirus and polioviruses. They have been linked with gastroenteritis, while some enteric viruses have also been implicated in more severe infections such as encephalitis, meningitis, hepatitis (hepatitis A and E viruses), cancer (polyomavirus), and myocarditis (enteroviruses). Therefore, this review presents information on the occurrence of enteric viruses of public health importance, diseases associated with human exposure to enteric viruses, assessment of their presence in contaminated water, and their removal in water and wastewater sources. In order to prevent illnesses associated with human exposure to viral contaminated water, we suggest the regular viral monitoring of treated wastewater before discharging it into the environment. Furthermore, we highlight the need for more research to focus on the development of more holistic disinfection methods that will inactivate waterborne viruses in municipal wastewater discharges, as this is highly needed to curtail the public health effects of human exposure to contaminated water. Moreover, such a method must be devoid of disinfection by-products that have mutagenic and carcinogenic potential.