In the first part of my dissertation I would like to study the metaphor itself, the definition of a metaphor and the different types of metaphors. Furthermore, in the first part, I would also like to present the difficulties of metaphor comprehension processing, the different theories of metaphor comprehension and the problems of the theories as well. In addition, I would like to define what the linguists, philosophers and scientists mean by literal meaning, figurative meaning and relevance theory. In the second part of my dissertation, what I would like to study is the metaphor comprehension process, first, by giving the definitions of the main keywords such as mental spaces, emergent structure, space structuring model and blending. I think knowing these notions are very important to understand what conceptual integration means and, of course, how it works. Secondly, I would like to present some eventrelated studies about how conceptual integration was examined in practice and the result of the researches. Finally, in the third part of my dissertation I would like to mention some other methods of how metaphors can be examined in cognitive science and philosophy.