Grammati̇cal category of case

Case is the immanent morphological category of the noun, showing the relations of the object to other objects and phenomena. In modern Eng is limited to the system of 2 cases: common & possessive which reflects the relations between words on the level of the phrase

The apostrophy serves to distinguish in writing the singular noun in the possessive case from the plural noun in the common case. The possessive of the most of plural nouns remains phonetically unexpressed: the few exceptions concern only some of the irregular plurals: e.g. the actresses' dresses, the children's room.

The Theory of Positional Cases
In accord with the theory of positional cases the unchangable forms of the noun may express different cases due to the functional positions occupied by the noun in the sentence. Thus, the English noun, on the analogy of classical Latin grammar, would distinguish, besides the inflexional posessive case, also the non-inflexional, i.e. purely positional cases: nominative, vocative, dative and accusative.

E.g. the nominative case: The letter is here. (subject to a verb)
the vocative case: (address) Are you ready, students?
the dative case: (indirect object to a verb) She gave the students some books.
the accusative case: (direct object and also object to a preposition) The books were given by the teacher.

The Theory of Prepositional Cases
According to it, combinations of nouns with prepositions on some object and attributive word-groups should be understood as morphological case forms. Here belong the dative case (to + noun, for + noun) and the posessive case (of + noun).

The Limited Case Theory
It is most broadly accepted among linguists at present. It was formulated by Sweet, Jespersen and was developed by Smirnitsky, Barkhudarov. It is based on the opposition of the possessive or posessive form as the strong member and the common, or “non-posessive” from as the weak member.

Postpositional Theory (No-Case Theory)
First, the postpositional element -'s is loosely connected with the noun, as it is used not only with single nouns, but also with whole word-groups. E.g. Somebody else's daughter. The blonde I had been dancing with's name was Bernice (Salinger). The girl in my class's mother.
Second, the 's can be attached to few nouns denoting living beings, in other cases the parallel prepositional construction is used.

Source
http://englishschool12.ru/publ/vse_dlja_ehkzamena/vse_dlja_ehkzamena/grammatical_category_of_case/65-1-0-10407