In this review study, we ask ourselves if decoherence theory can solve the problems of measurement in quantum mechanics. After an introduction to decoherence theory, we present the problem of preferred basis, the problem of non-observability of interference and the problem of definite outcomes. We present Zurek's theory of environment induced superselection rules and find that the problem of preferred basis and the problem of non-observability of interference can be solved through decoherence theory, but not the problem of outcomes, if we accept the eigenstate-eigenvalue link and the Born statistical interpretation. We reveal that these two concepts are essential in the Copenhagen interpretations of quantum mechanics, and give an account for von Neumann's and Wigner's conscious collapse interpretation as well as a detailed description of Bohr's and Heisenberg's interpretation. We discuss how Bohr's and Heisenberg's interpretation relates to decoherence with a special emphasis on the irreducibility of classical concepts as interpreted by Don Howard. During the discussion, we critique Wigner's use of the word "consciousness" as opposed to von Neumann's use, as well as Howard's decisively ontological approach to Bohr through an antithetical Kantian approach. We conclude by stating that decoherence theory cannot decisively solve the problem of definite outcomes of quantum mechanics, even when considering it in relation to the Copenhagen interpretation.