Figures of speech, such as metaphor and irony, are ubiquitous in literature works and colloquial conversations. This poses great challenge for natural language understanding since figures of speech usually deviate from their ostensible meanings to express deeper semantic implications. Previous research lays emphasis on the literary aspect of figures and seldom provide a comprehensive exploration from a view of computational linguistics. In this paper, we first propose the concept of figurative unit, which is the carrier of a figure. Then we select 12 types of figures commonly used in Chinese, and build a Chinese corpus for Contextualized Figure Recognition (ConFiguRe). Different from previous token-level or sentence-level counterparts, ConFiguRe aims at extracting a figurative unit from discourse-level context, and classifying the figurative unit into the right figure type. On ConFiguRe, three tasks, i.e., figure extraction, figure type classification and figure recognition, are designed and the state-of-the-art techniques are utilized to implement the benchmarks. We conduct thorough experiments and show that all three tasks are challenging for existing models, thus requiring further research. Our dataset and code are publicly available at https://github.com/pku-tangent/ConFiguRe.