The developers at Whatsapp has now added support for Chrome Browser. Smartphone users can now update their apps and use Whatsapp from Chrome based website.
Currently only Google Chrome is supported and you need to update Chrome to V36+ in order to access Web based Whatsapp and your smartphone App and scan the QR Code on web.whatsapp.com . After opening all you chats will be accessible and it is recommended to have WiFi connection for minimal data loss.
This is supported by Android, Windows Phone, Blackberry and Nokia Symbian Platform. As you have probably noticed iOS is out of list due to limitations of iOS platform and they are working on a way around.
How to enable Whatsapp Web on Android
Currently some Android users are having problem as even after update some users are unable to see the option to scan QR Code and to solve the issue just uninstall the Whatsapp app and re-install to have the web version working.