We study the framework of quantum resource theories, especially concerning quantum coherence. Understanding the role of coherence in information processing has extended our knowledge toward quantum information theory beyond classical theories. Recently studied resource theories of quantum coherence provide us with a powerful tool to characterize a quantum state which is useful to perform nonclassical tasks and to quantify the amount of quantum resource contained in it. We first study how a quantum resource theory can be constructed by choosing the appropriate set of free (incoherent) states and free (incoherent) operations. Then, faithful measures so-called monotones are introduced to quantify the amount of quantum (coherence) resource, which cannot be generated from free states and does not increase by free operations. Finally, we establish connections between the resource theory of coherence and other kinds of quantum resource theories of entanglement and nonclassicality.