Language is a unique human cognitive ability that allows us to communicate ideas and thoughts, and in no other species do we find a communication system which is that complex. This complexity is represented in the arrangement of the brain’s language-processing areas. Even though the left hemisphere, especially the two main centers called Broca’s area and Wernicke’s area, dominates when it comes to language comprehension and expression, many other regions of the brain contribute to the cognitive process that is language. The last decades offered insight into the location and function of the language system thanks to the study of language disorders, which connected the data summoned from the examination of damaged brains to the specific linguistic functions of the affected areas in the normal brain. When it comes to the organization of language in the brain, another interesting point would be language acquisition, a process that is known to be extremely prolific during early childhood, but stagnates after the onset of puberty. It is a crucial task of researchers to determine the reasons of this phenomenon in terms of brain plasticity. This paper will give an overview of the brain’s main language-processing regions and their respective functions. Another point will be the examination of the role of brain plasticity in the process of language acquisition. Finally, the most important language disorders will be introduced and explained.