Traditional Chinese Painting (TCP) is an invaluable cultural heritage resource and a unique visual art style. In recent years, increasing interest has been placed on digitalizing TCPs to preserve and revive the culture. The resulting digital copies have enabled the advancement of computational methods for structured and systematic understanding of TCPs. To explore this topic, we conducted an in-depth analysis of 92 pieces of literature. We examined the current use of computer technologies on TCPs from three perspectives, based on numerous conversations with specialists. First, in light of the "Six Principles of Painting" theory, we categorized the articles according to their research focus on artistic elements. Second, we created a four-stage framework to illustrate the purposes of TCP applications. Third, we summarized the popular computational techniques applied to TCPs. The framework also provides insights into potential applications and future prospects, with professional opinion. The list of surveyed publications and related information is available online at https://ca4tcp.com.