The moon illusion is one of the most ancient and persistent questions of natural philosophy. The investigation of this phenomenon has played a crucial role in the genesis and ongoing development of the field of perception, being a major point of consideration for Ptolemy, Alhazen (Ibn al-Haytham), Leonardo da Vinci, Descartes and George Berkeley. Relatively recent empirical studies have focused on explanations of the illusion created by contrast with the horizon (Ponzo illusion). However, a careful review reveals that the far more dramatic appearance of the moon illusion still remains unsolved. This paper takes a historical view of the explanations over three major paradigms: the classical, the experimental, and the modern perceptual theories. The natural tension between mathematics and observation is also a sub-plot.