WhatsApp has announced the launch of WhatsApp Web. This service is accessible for WhatsApp Android, Windows or Blackberry users (that's right, no iPhone!), through the Google Chrome desktop browser only. Plans for adding support for other desktop browsers or WhatsApp for iPhone are not known.
Navigate to https://web.whatsapp.com. A QR code will be splashed on the desktop screen. This code must be scanned using the WhatsApp app on your mobile. Instructions for locating the "Scan QR Code" option is displayed on the web page.
An update to WhatsApp will be needed before this feature becomes available.
As of now, the WhatsApp Android update for this feature still hasn't been rolled out.
Update Jan 22: The Android update has been rolled out.