Kerimil, user on Arduino Forum, submitted us his  project which focuses on establishing communication between an Arduino board and an android mobile using Bluetooth®:

The idea is to gain access to hardware on Android devices (accelerometers, gyro, wifi connectivity, gps, GPRS, touchscreen, text to speech and speech to text) and/or use it to relay data to the internet. MIT’s app inventor was used to write a custom app in this example. The code can be easily modified to create your own apps.

You can watch his video below and read the complete tutorial on this page.