In cognitive approaches to metaphor, the framework of Relevance Theory (RT) has been attracting more and more scholarly attention. Classic RT argues that metaphors are used to convey a series of strong or weak implicatures, while new RT holds that metaphoric meaning should be attributed to explicatures. This paper points out that the research on metaphor under the framework of RT faces many controversies and challenges concerning issues such as the emergent issue, the circular issue in methodology, the motivation of metaphor, the compatibility with other research theories, empirical studies, and the diversity of data. The paper also presents possible developments in this field in the future.