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Vector databases, known for their versatility, performance, scalability, and efficient algorithms, store data as high-dimensional vectors, representing a wide variety of data such as text and images. They are used for AI applications and have gained popularity in the industry, with Pinecone being named the most popular vector database across industry reports and the only vector database on the inaugural Fortune 2023 50 AI Innovator list. Additionally, there is a discussion on how vector databases relate to search, indicating their relevance in various applications.