WhatsApp, yesterday night, announced its Web client for the PC and Mac users, however, for Android users only. This web client would mirror conversations and messages from the phone to the web client, which means messages would remain on the phone as well.
This feature would not work for iPhone users because of limitations Apple places. Also, at the moment it only supports Google’s Chrome browser.
To get WhatsApp working on your PC or Mac, you would first have to go to https://web.whatsapp.com. That will open a QR code that you would need to scan from WhatsApp on your phone to pair the two instances.