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.

IntroductionBluetooth® Low Energy (Bluetooth® LE or BLE) is a low-power, short-range wireless communication technology that is ideal for use on the Internet of Things (IoT). BLE is designed for ...

An Android* phone or tablet running Android and has Bluetooth. Connect your Intel® Edison board to a Wi-Fi* network, see Get started with Intel® Edison technology.

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 ...

Thanks to the LightBlue Bean+, however, one of those roadblocks has been torn down. The Bean+ is basically an Arduino board that can be programmed via Bluetooth LE.

The $22 kit includes an Arduino-BLE board and 6-pin header that should be fairly broadly applicable for building Arduino-based hardware that can communicate with iOS devices.

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.