Android Jetpack Compose is a modern toolkit for building native UI on Android, simplifying and accelerating UI development with less code, powerful tools, and intuitive Kotlin APIs. To develop with Jetpack Compose, download Android Studio Arctic Fox and create a new project or import a sample app from GitHub. Testing Jetpack Compose layouts involves finding elements, verifying attributes, and performing actions using Espresso or the Compose testing APIs, which provide advanced features like time manipulation. A test class can be created to verify that the counter text displayed is correct and that the counter increments correctly when the button is clicked. To run these tests on a CI server like Bitrise, create a new project, set up repository access, and configure the build configuration, then add steps for building, testing, and deploying the app, including using Firebase Test Lab to run UI tests.