Describe a strategy for managing and deploying a web application that has to support multiple browsers and versions.

Cross-browser compatibility is crucial for web applications. Cross-browser testing ensures functionality across various browsers. Progressive enhancement starts with core functionality and enhances for each browser. Graceful degradation designs for the newest browser, providing basic functionality for older ones. Feature detection adapts the UI based on browser capabilities. The chosen strategy depends on project requirements, user base, and the desired balance between providing advanced features and supporting a wide range of browsers.