A nonmineral (mineralogy) is a substance found in a natural environment that does not satisfy the definition of a mineral and is not even a mineraloid. Many non-minerals are mined and have industrial or other uses similar to minerals, such as jewelry.
To be classified as a "true" mineral, a substance must be a solid, arising from geological processes, and having a crystal structure. Traditionally, it must also be an inorganic, naturally occurring, homogeneous substance with a defined chemical composition, but now organically derived substances that have been transformed into a crystalline structure are minerals.
Synthetic diamond, not naturally occurring like most other synthetic gems, but difficult to distinguish from naturally occurring forms.
Vulcanite, vulcanized natural or synthetic rubber, thus not a mineral due to organic composition, lack of crystal structure, and not naturally occurring.
Water, a liquid (but naturally occurring ice is a mineral).
Other considerations
Some minerals, such as the well-known Apatite and Mica, are not homogeneous substances, but are a mixture of related minerals, sometimes referred to as a mineral group.