This Bluetooth module ties directly into the Tx and Rx lines of the Arduino so a wireless serial connection between an Android device can be established.

Instructables user ASCAS shows off how to add voice control to your Arduino projects using your Android phone and Bluetooth. The Arduino gets a Bluetooth attachment and a set of code.

This project incorporates communication between an Android Phone and the Arduino using Bluetooth. The basic functionality includes taking messages from an android phone, displaying them on an LCD ...

Makers, developers and hobbyists that are looking for a low-cost Bluetooth Arduino compatible micro controller that can be controlled and programmed ...

To control the Arduino he’s using ArduDroid with a Bluetooth module. The app lets you trigger the various digital and analog outputs, and send and receive data.

For now, it's only possible to connect to an Arduino board through USB via an OTG cable, but joaomcgd says he plans on adding support for Bluetooth or Wi-Fi receivers in the future.