IPhone Do not disturb settings?

If I put my phone iPhone 4 on Do Not Disturb, is there any way I can set it so that certain people's texts/calls come through? In case I don't want to be disturbed by emails or other texts but want to know if certain people are trying to contact me.

Yes, open Settings -> Notifications -> Do Not Disturb -> Allows Call From and then select who you want to allow calls to still come in from.