Plato mentions them as of pre-socratic origin, a list created by the philosopher Empedocles.
One classic diagram is to place a two squares on top of each other with the corners of one being the classical elements, and the corners of the other being the properties.
These elements were used by Galen in describing the human body with an association with the [four humours]?: phlegm?, [yellow bile]?, [black bile]?, and blood?.
Some cosmologies include a fifth element, ether, and some chinese cosmologies include metal? and wood? but exclude air.
The Chinese elements correspond to the brighter planets visible with unaided eyes in the night sky: Metal (Venus), Wood (Jupiter), Water (Mercury), Fire (Mars), Earth (Saturn). Air from Plato's system was not part of the Chinese system. The Moon represents Yin, The Sun represents Yang. Yin Yang, and the five elements are topics in I-Ching which obviously was related to Chinese cosmology and astrology.
Some South Asian tradition also includes the air, earth, fire, water distinctions.