This paper reviews selected studies and discussion which address the evolution of semantics and syntax. The focus is on psycholinguistic and neurolinguistic literature. Many problems were observed in the literature: lack of empirical studies, lack of communication between experts coming from different scientific fields and lack of linguistic studies and discussions. Converging evidence suggests that language exapted from pre-existing cognitive domains, a claim which stands opposed to the modular theories of language emergence. Furthermore, some animals demonstrate certain levels of semantic and syntactic capacity in their vocal communication systems. Studies in lexical semantics show that word meaning is embodied, i.e. that it is dependent on sensorimotor information. The most embodied word meanings are those of action and concrete words, compared to abstract words which show lower levels of embodiment. Nevertheless, it is possible that abstract words phylogenetically arose from concrete words. It also seems possible that particular aspects of syntax are embodied. Semantically transitive events seem to demonstrate the highest levels of embodiment. However, there are also arguments that the processing of syntactic transitivity is also at least partially embodied. Additionally, many studies highlight the rule of agent i.e. subject salience according to which the agent i.e. subject typically takes the first sentential slot in particular sentence types. This is confirmed by the dominant frequency of the word orders SOV and SVO in the world languages, the cognitive salience of the agent during the processing of semantically transitive events, prevalence of nominative–accusative languages compared to ergative–absolutive languages and neurophysiological studies which show that the first syntactic constituent is automatically interpreted as an agent until the morphosyntax of the sentence shows otherwise. It is possible that the agent/subject salience rule is the result of the ways in which Broca's area processes prototypical transitive events. In the last part of the paper the progolanguage model and the theory of language fossils are discussed, however, no clear conclusions can be drawn. Finally, this literature review supports the hypothesis that semantics and syntax evolved gradually through exapation from specific pre-existing cognitive domains and that both semantics and syntax are in some phylogenetic connection with animal communication systems.