Testing Progressive Web Apps involves evaluating various aspects across different browsers, devices, and configurations to ensure they work as expected. This includes testing the manifest file to check icons and launch URLs display correctly, testing service workers to verify caching and updates work properly, and testing responsiveness on various screen sizes and orientations. Accessibility is also important to test using tools like Lighthouse, Axe and WAVE to meet WCAG standards. Considering real-world network conditions and unsupported browsers is also recommended during testing.