WhatsApp is testing a web client, according to screenshots shared in unofficial WhatsApp community by a Mexican user. WhatsApp Messenger screenshots in Spanish shows the instructions to use the web client. This will work like Airdroid or other clients that offers remote web access.
According to the screenshots, you need to go to web.whatsapp.com and scan a QR code using WhatsApp. Web.whatsapp.com is protected with a Google account even though WhatsApp is now owned by Facebook. This is likely to be used by testers as of now and it might use custom or Facebook account to log in when it releases. Once you are connected, you can see the chats on your browser. You can also see the session from the web client on your app and also clear previous session.
WhatsApp version 2.11.471 for Android was rumored to have had string of codes that mention WhatsApp Web. Now the Android app has been updated to version 2.11.491, still we have not seen the web client.
WhatsApp Call is expected to release sometime in Q1 2015. We had seen several leaked screenshots of WhatsApp Voice Calls in recent months. Looks like the web client might come first before the voice calling feature.