Early debates on the nature of matter centered on identifying a single underlying principle (Monism): water was claimed by Thales, air by Anaximenes, Apeiron (meaning "the undefined infinite") by Anaximander, and fire by Heraclitus. Democritus conceived an atomic theory (Atomism) many centuries before it was accepted by modern science.
The nature of the mind and its relation to the body has also exercised the best brains for millennia. There is a large overlap here with Philosophy of Mind, which is the branch of philosophy that studies the nature of the mind, mental events, mental functions, mental properties and consciousness, and their relationship to the physical body.
In the 17th Century, Descartes proposed a Dualist solution called Substance Dualism (or Cartesian Dualism) whereby the mind and body are totally separate and different: the mental does not have extension in space, and the material cannot think.
Idealists, like Bishop George Berkeley and the German Idealist school, claim that material objects do not exist unless perceived (Idealism is essentially a Monist, rather than Dualist, theory in that there is a single universal substance or principle).
Baruch Spinoza and Bertrand Russell both adopted, in different ways, a dual-aspect theory called Neutral Monism, which claims that existence consists of a single substance which in itself is neither mental nor physical, but is capable of mental and physical aspects or attributes.
In the last century, science (particularly atomic theory, evolution, computer technology and neuroscience) has demonstrated many ways in which mind and brain interact in a physical way, but the exact nature of the relationship is still open to debate. The dominant metaphysics in the 20th Century has therefore been various versions of Physicalism (or Materialism), a Monist solution which explains matter and mind as mere aspects of each other, or derivatives of a neutral substance.