Possession may be marked in many ways, such as simple juxtaposition of nouns, possessive case, possessed case, construct state (as in Arabic, and Nêlêmwa), or adpositions (possessive suffixes, possessive adjectives). For example, English uses a possessive clitic ('s), a preposition, of, and adjectives (my, your, his, her, etc.). Predicates denoting possession may be formed using a verb such as English have, or by other means such as existential clauses (as is usual in languages such as Russian).
There are many types of possession, but a common distinction is alienable versus inalienable possession. Alienability refers to the ability to dissociate something from its parent; in this case, a quality from its owner.
When something is inalienably possessed, it is usually an attribute: for example, John's big nose is inalienably possessed, because it cannot (without surgery) be removed from John; it is simply a quality he has. In contrast, 'John's briefcase' is alienably possessed, because it can be separated from John.
Many languages make this distinction as part of their grammar - typically, using different affixes for alienable and inalienable possession. For example, in Mikasuki (a Muskogean language of Florida), ac-akni (inalienable) means 'my body', whereas am-akni (alienable) means 'my meat'. English does not have any way of making such distinctions (the example from Mikasuki is clear to English speakers only because there happen to be two different words in English that translate -akni in the two senses: both Mikasuki words could be translated as 'my flesh', and then the distinction would disappear in English).
Possessive pronouns in Polynesian languages such as Hawaiian and Maori are associated with nouns distinguishing between o-class, a-class and neutral pronouns according to the relationship of possessor and possessed. O-class possessive pronouns are used if the possessive relationship cannot be begun or ended by the possessor.
Obligatory possession is sometimes called inalienable possession. Inalienable possession is a semantic notion, i.e., largely dependent on the way a culture structures the world, while obligatory possession is a property of morphemes. In general, nouns with the property of requiring obligatorily possession are notionally inalienably possessed, but the fit is rarely, if ever perfect.