Forms of subject
The subject of a sentence is sometimes defined as the argument that generally refers to the origin of the action or the undergoer of the state shown by the predicate. This is a semantic definition. Such a definition is problematic for several reasons. In languages where a passive voice exists, the subject of a passive verb may be the target or result of the action. For example:
John was arrested.
The police arrested John.
In the first sentence (which is in the passive voice), John is the subject, while in the second sentence (active voice) the police is the subject and John is the object. Similarly, some verbs can be used both as transitive and as intransitive. An example is the English verb break:
John broke the chain.
The chain broke.
In the first sentence, the chain is the object, while in the second, it is the subject. But the relation of the chain to the event described by the sentence is the same in the two cases. This can be seen by considering the fact that the two sentences can be used to describe the same situation: Whenever the first sentence is true, the second one will be true, as well.
Some linguistic theories require every language to have a category of subject. However, there is no such category that is consistent for all languages.
In many languages, the subject triggers agreement morphology on the verb or auxiliary of a sentence. For example, in English one uses the form has for sentences with a singular subject, and have in sentences with a plural subject. This is a morphosyntactic definition.
She has left.
They have left.
This definition works fairly well for English, except in the case of verbs that do not agree. Examples of English verbs that never carry agreement include the modals must, can, will, might, may. The subject in English can also be identified by the fact that the interrogative clause is formed by inverting the normal subject–verb word order to verb–subject. Thus:
You won't call me.
Won't you call me?
In many languages that mark case on the arguments of a verb, the topic of the conversation tends to be placed in the nominative case, and this combination is termed the subject. Such a morphological definition is inherited from classical times. However, sometimes the subject may carry other cases, like the dative, so this definition is not perfect. Not all languages have a nominative case, and for many of these this concept of subject does not work at all: in ergative-absolutive languages neither core case, absolutive or ergative, carries the topic the way the nominative does in many nominative-accusative languages. Different theoretical traditions have treated both as subject at different times, but with no agreement.
In languages that lack verb agreement and morphological case marking, one must define the nominative case (if there is one) in terms of word order. For example, in Mainland Scandinavian (Norwegian, Swedish and Danish) the subject occurs either right in front of the tensed verb of a sentence, or follows the verb but precedes the object.
Finally, the subject tends to be the topic of the proposition. In languages with no other means to mark a topic, making an object into a subject by using passivization (I did it → it was done) is a way to topicalize said object. (See also topic-prominent languages.)
Some languages can omit the subject if it is recoverable from the context of utterance (null subject language). Many of these languages have rich subject-verb agreement (e. g. Italian) while others have no subject-verb agreement at all (Mandarin Chinese). The term pro-drop language is used for languages where pronouns can be omitted more generally, i.e. even when they are not a subject.
In some languages, like English or French, sentences must have a syntactical subject, either a noun or noun phrase, or a pronoun, even if the sentences do not have a semantic subject. This is why verbs like rain must carry a "subject" such as it, even if nothing is actually "doing" the raining. It is in this case an expletive and a dummy pronoun.

Subject orientation
It is generally assumed that the Noun Phrase occurring with the Verb Phrase, constituting a sentence, is a subject. Copular sentences challenge this view. In a particular class of copular sentences, called "inverse copular sentences", the noun phrase which occurs with the verb phrase plays the role of predicate, occupying the position which is canonically reserved for subjects, and the subject is embedded in the verb phrase (cf. copula). This can be exemplified by pairs of sentences like these pictures of the wall are the cause of the riot (where the preverbal Noun Phrase plays the role of subject and the post-verbal one plays the role of predicate) vs the cause of the riot is these pictures of the wall (where the order is inverse). This has far reaching consequences, affecting for example the theory of expletive subjects and unaccusative verbs (cf. Moro 1997 and Hale - Keyser 2003 and references cited there).