Order Notifications

Not sure if I'm missing something obvious.

Should an admin receive email notifications when orders are placed? I believe the customer is receiving notifications regarding the order. Should admins be bcc'd, or should a copy of the same email go to an admin?

I noticed much like when new plugins are available, the dashboard indicates that new orders have been placed, but sometimes I will go a day or two without checking the dashboard. Is it possible to be notified as soon as an order is placed?

Thanks in advance.