Agile testing has to work with the Agile lifecycle and processes adopted by your team. For example, if you adopt the Scrum methodology, that means you will have to conduct your testing within the Sprint cycles. Agile is about incremental development. So small pieces of functionality are delivered during each iteration. The challenge here is to ensure that new functionality does not break existing functionality. The typically shorter iteration duration of Agile methodology makes this more demanding.
Agile teams have typically tried to adopt Test-Driven Development (TDD) as a solution for testing needs. This is a good solution in many respects, but care has to be taken to implement TDD properly. For example, discussions about TDD usually tend to focus on unit test coverage, which is a major subset, but not the only aspect of testing. Automated testing should also cover system-level testing and workflows that cover functionality across multiple modules. 100% code coverage may sometimes be misleading because workflows may require additional tests.
Note also that automated testing is not the entirety of testing either. Performance testing, user interface testing, etc. are other aspects of testing that sometimes require manual effort both from the development team as well as from customers. Much of this requires time as in calendar time. Even running an entire suite of automated tests for a large product requires time. If you have teams working across the clock in different geographic regions, you may not get the luxury of downtime for automated tests to run at “night”.
All this points to better management of the iteration cycle. Management includes project management in terms of setting the necessary time to run through necessary regression tests, which may include a battery of automated tests and manual testing. The manual testing may involve full regression or segmented regression. Configuration management is also necessary to ensure that the right pieces are being tested and deployed. The larger the project gets, the more important it is to get better quality tools and implement better processes to keep a handle on things.