WhatsApp is working on a feature for synchronizing chats between iOS and Android (or vice versa), according to ABetaInfo.
For the time being, it appears that users can access their entire history on four different devices with only one account (linked to a phone number). This probably requires wifi.
Several other applications already incorporate a similar feature, including Facebook Messenger and Slack. The big difference with those apps is that they use a connected email address, while WhatsApp uses a phone number as a way to log in.
WhatsApp on iPad
ABetaInfo asserts that there is no release date for the feature as of yet. Over a year ago, it turned out that an iPad version of WhatsApp was being created, and it probably requires the synchronisation feature in order to function. This puts the release of the iPad version of WhatsApp after the release of the synchronisation feature.
The only thing that keeps missing is way to login with multiple phone numbers.