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Predicting the visibility of the lunar crescent drew great attention during the Middle Ages, especially among Muslims, because the dates of religious practices in Islam and calendars, in addition to being aware of the motion of the moon in its orbit, are based on the lunar month.
This paper aims to study the development of crescent visibility criteria from ancient times through the medieval period to the modern update. Some basics and astronomical terms related to crescent visibility are presented and then a comprehensive view of crescent visibility criteria is examined by surveying about 54 published research papers related to the issue of crescent visibility. Each research paper is summarized, classified, and the results evaluated. Also, the previous studies are divided into two parts, including the ancient and medieval ages, which depend on the visual observations of the naked eye. We found that predicting the crescent's visibility started at the end of the Islamic era. The second part shows that at the beginning of the twentieth century, engineering criteria were introduced into research for the prediction of crescent visibility, then physical engineering criteria, weather conditions, and observer location on the Earth's surface were introduced. Currently, modern technologies have been introduced, such as CCD cameras and image processing technology. The study concludes that there are no 100% accurate criteria that correspond to the truth and completely match the observations, as these criteria need improvements by increasing the number of observations and introducing modern technologies to the crescent's visibility prediction.