Background checking... Do I need to do anything or just waiting?

It's been more than 1 week for my background check. I haven't heard anything from my new employer since then. Do I need to do anything like Follow Up or just waiting? Ohh, They called me once for a simple question on last Thursday.

Getting nervous... When they called me and gave me the oral offer, they want me to start ASAP, no later than the middle of Aug. My current employer requests 2 weeks notice.... BTW, I am a banking officer. What should I do now?

Please advise. Thanks in advance!