How are drush and jenkins used together for continuous integration?
For my projects, I use a build script made of Drush commands in a Jenkins job. I use my Phing Drush Task project to run Drush from a Phing build script. This allow me to leverage the existing Phing tasks (eg. files copy, phplint, etc.). With the help of Drush, this build script


Downloads all non-custom code (ie. Drupal core and contribs module and themes) with Drush Make to ./dist
Expands placeholders in a versioned settings.php (ie. replace ${db_host} with the actual DB hostname) while copying it to the freshly downloaded ./dist/sites/default folder.
Copy custom modules and themes to ./dist/sites/all/modules/custom and ./dist/sites/all/themes/custom
Run phplint for all files from my custom modules and themes.
Copy everything under ./dist to a pre-configured webroot.
Run drush site-install testing and drush pm-enable simpletest to install a fresh site using the build code base and able to run SimpleTest.
Run drush test-run to run my custom module test suites.
Run drush coder-review.


Here is a commented build.xml template for Drush usage in Jenkins.