OpenAPI provides a comprehensive framework for utilizing different types of parameters—path, query, header, and cookie—each serving specific purposes in API design. Path parameters are used to identify specific resources in RESTful APIs and must match the placeholder in the path entry, though their visibility requires careful consideration to avoid confusion. Query parameters offer flexibility for optional values and are commonly used for tasks like filtering, sorting, and pagination; good design involves setting sensible defaults that can be optionally modified. While cookies are generally not recommended in APIs, they can be supported for legacy systems, but using an API key in a header is a preferred alternative. Header parameters are effective for delivering metadata separate from the payload, such as client identification and tracing, and are case-insensitive. Successful API parameter design involves understanding whether a parameter is optional or required, if it relates to the data, and considering the client's needs, ensuring a robust, long-lived API.