A number of users have been complaining about crashes with Battlefield 4, particularly on systems with AMD graphics cards and Windows 8. AMD had promised that it would fix the crashing, and as said, it has delivered.
The new Catalyst 13.11 Beta8 driver should have fixed the crashes that users are experiencing. As with most drivers, it contains all the extra goodies of the previous driver release.
The driver has support for Windows 7 and above machines, paired with HD 5000 series and above graphics cards, of course including the new R9-290X graphics card. It is available for download here.