Metaphor is a figurative language that has been frequently used in our daily lives. Due to its significance for downstream natural language processing tasks, such as machine translation and sentiment analysis, computational metaphor processing has set off an upsurge in the community. With the development of Artificial Intelligence, an increasing number of technological tools and frameworks have been proposed in this domain. In this article, we aim to comprehensively summarize and categorize previous computational metaphor processing approaches regarding metaphor identification, interpretation, generation, and application. Meanwhile, we compare the strengths and weaknesses of current works and conceive future directions in this field.