In ontology and the philosophy of mind, a non-physical entity is a spirit or being that exists outside of physical reality. Their existence divides the philosophical school of physicalism from the schools of idealism and dualism; with the latter schools holding that they can exist and the former holding that they cannot. If one posits that non-physical entities can exist, there exist further debates as to their inherent natures and their position relative to physical entities.
Philosophers generally do agree on the existence of abstract objects. These include concepts such as numbers, mathematical sets and functions, and philosohpical relations and properties. Such entities are not physical inasmuch as they exist outwith space and time. An abstract property such as redness has also has no location in space-time. Whilst older Cartesian dualists held the existence of non-physical minds, more limited forms of dualism propounded by 20th and 21st century philosophers (such as property dualism) hold merely the existence of non-physical properties.
The dualist school acknowledges the existence of non-physical entities, the most widely discussed one being the mind. But beyond that it runs into stumbling blocks. Pierre Gassendi put one such problem directly to Descartes in 1641, in response to Descartes's Meditations:
[It] still remains to be explained how that union and apparent intermingling [of mind and body …] can be found in you, if you are incorporeal, unextended and indivisible […]. How, at least, can you be united with the brain, or some minute part in it, which (as has been said) must yet have some magnitude or extension, however small it be ? If you are wholly without parts how can you mix or appear to mix with its minute subdivisions ? For there is no mixture unless each of the things to be mixed has parts that can mix with one another.
Descartes' response to Gassendi, and to Princess Elizabeth who asked him similar questions in 1643, is generally considered nowadays to be lacking, because it did not address what is known in the philosophy of mind as the interaction problem. This is a problem for non-physical entities as posited by dualism: by what mechanism, exactly, do they interact with physical entities, and how can they do so? Interaction with physical systems requires physical properties which a non-physical entity does not possess.
Dualists either, like Descartes, avoid the problem by considering it impossible for a non-physical mind to conceive the relationship that it has with the physical, and so impossible to explain philosophically, or assert that the questioner has made the fundamental mistake of thinking that the distinction between the physical and the non-physical is such that it prevents each from affecting the other.
Other questions about the non-physical which dualism has not answered include such questions as how many minds each person can have, which is not an issue for physicalism which can simply declare one-mind-per-person almost by definition; and whether non-physical entities such as minds and souls are simple or compound, and if the latter, what "stuff" the compounds are made from.
Describing in philosophical terms what a non-physical entity actually is (or would be) can prove problematic. A convenient example of what constitutes a non-physical entity is a ghost. Gilbert Ryle once labelled Cartesian Dualism as positing the "ghost in the machine".  However, it is hard to define in philosophical terms what it is, precisely, about a ghost that makes it a specifically non-physical, rather than a physical entity. Most tellingly, were the existence of ghosts ever be demonstrated beyond doubt, in terms of the physicalist/dualist philosophical debate (at least) that would actually place them in the category of physical entities.
Purported non-mental non-physical entities include things such as gods, angels, and ghosts. As aforementioned, a demonstration beyond doubt of their existence(s) would place them in the realm of the physical, as far as physicalist/dualist metaphysics is concerned. Lacking such demonstrations, their existences and natures are widely debated, independently of the philosophy of mind.
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