The problem of the irreducibility of mind, also known as the problem of consciousness, refers to “the irreducibility of the concepts of mind into the concepts of physics.” In short, “the objective concepts of physics are incapable of explaining completely the subjective phenomena of mind.” This is one of the most popular topics in the western world of philosophy. The mind-body problem has puzzled many great thinkers, ever since Descartes introduced the mind-matter dualism. Now the study of the mind-body problem has found its core to be the problem of consciousness, which seems to be more important nowadays when brain science is progressing quickly. The purpose of this paper is to make a detailed analysis and explanation about this problem and introduce the major academic schools in this field.