F-Droid is an app store for Android where only open source applications are available for free. It provides an alternative to the proprietary Google Play Store, which is where most Android app distribution currently takes place. Because the Google Play Store is where most users go to find and install apps, this gives Google the power to exercise control over Android app developers. In this blog post, I describe the design, mechanism and results of this control from the perspective of a long-time Android app developer.
also worth pointing out that fdroid supports reproducible builds, which helps quite a bit with being trustable.