Linguistics is already an interesting field. It has the unique disposition of branching out into various interdisciplinary fields, such as computational linguistics (computer science and linguistics), sociolinguistics (sociology and linguistics), and psycholinguistics (psychology and linguistics). This allows it to be regarded at times as part of the social sciences, humanities, and cognitive sciences.

Psycholinguistics, however, is arguably the most fundamental of all the interdisciplinary fields. Psycholinguistics focuses primarily on language acquisition. It aims to provide a fairly universal theory to how our brains acquire language and comprehend it.

Studying those who have aphasia, a language disorder that limits speech and language comprehension, in contrast to those unaffected has been instrumental in understanding the relationship between psychology and language.

One of the more recent linguistics theories that was considered revolutionary for its time (though still not entirely accepted amongst the linguistics community) was linguist Noam Chomsky's in the 1950s. He provided a modern take on "universal grammar." He posited that language acquisition was innate, that we were genetically and biologically programmed to psychologically acquire the ability to understand and speak a language within the grammatical confines (the environment shapes the specifics), as opposed to a kind of brute force memorization. This pre-wired brain facilitates the psychological process.

The relationship is a complex one, so multifaceted in fact that the study called "psycholinguistics" is devoted to it.  The basic divisions of that discipline are how words mean (that is, how does the mind connect the sound of a word with its signified object, abstraction, or idea); syntax (how does the mind assemble a series of sounds into a sentence); discourse (how does the mind process an exchange of sounds into an exchange of ideas, opinions, etc).   So the way spoken language works is the primary relationship.  Also, written language and its mental processes can be considered part of psycholinguistics.