The HC-05, a Bluetooth to serial bridge ... especially if you will be using modules from different sources. They don’t always come with the same firmware.

It’s hard to imagine an easier way to set up communications between an Android device and an Arduino using Bluetooth ... see the cheap and ubiquitous HC-05 Bluetooth module.

Android apps for Arduino ... using a serial interface. This works well if your board connects to your computer via a USB cable and a USB-to-serial chip, but some applications might require a wireless ...