Water is one of the most important natural resources for all living organisms, including humans. Water consumption is increasing over the years as a result of the increase in the number of people, and at the same time, the causes of pollution of surface water sources increase. Water pollution is one of the most important causes of diseases and the transmission of infection to the organisms that use it. Also, the quality of agricultural crops is linked to the quality of the water used for irrigation. As a result, there was a need to monitor and evaluate the main water sources to maintain the quality of their water suitable for use by humans and other organisms. As is well known, it is difficult to evaluate the water quality of large samples with concentrations of many parameters using traditional methods, which depend on comparing experimentally determined parameter values with current standards. As a result, over the past century and the present, many methods of assessing water quality have emerged. This research aims to introduce the most important indices of water quality used at present to assess the quality of surface water for drinking and irrigation purposes, as well as the history of these methods and their development over time and their most important advantages, in addition to a group of the most important research that used these methods during the past few years.