Which version does React Native support (iOS and Android)?

android ios react-native mobile-application mobile-development

You can run it on minSdk 21 as it is documented on the framework's github page.

React Native apps may target iOS 11.0 and Android 5.0 (API 21) or newer.

android ios react-native mobile-application mobile-development

for February 2020:
React Native apps may target iOS 10.0 and Android 4.1 (API 16) ornewer.
Expo supports Android 5+ and iOS 10+.