Leveraging established Web technologies and advanced standards for Thing Descriptions (TDs), TWIST introduces a WoT Proxy architecture that successfully bridges the gap between the Internet of Things (IoT) and the existing Web. TWIST uses OpenAPI for REST APIs and AsyncAPI descriptions for asynchronous APIs enabling unified handling of services and Things in applications. The Proxy communicates with real-world devices via gateways (translating low-level IoT protocols to high-level) and with the World Wide Web. It publishes their descriptions and APIs within plain HTML pages enriched with JSON-LD. This simplifies incorporating Things into the Web and Semantic Web, improves their discovery by Web crawlers, and allows clients to search for and interact with them seamlessly.