Usually the iPhone employs a Visual Voicemail service. When you open up your Phone feature on your iPhone you will see Voicemail at the far right end of the lower task bar, just to the right of the phone Keypad. Here is where you will have all of your voicemails listed, and those that have not been listened to will have a blue dot to the left of them.
There will also be the name of the person if you have their contact in your Contacts List, and if not it will just be their number. Now you can see where they are calling from and what type of phone it is, if you have entered it into their contact. Here you can select the voicemail you want to listen to and then listen to it, or hit the Call Back button if you want to return the call.
There is also a Delete button that you can hit once you have highlighted the voicemail you wanted to delete. This format is what the iPhone Visual Voicemail is, though this Visual Voicemail is not available for absolutely everyone. If you do have it the number indication on the Phone icon on the iPhone's desktop will include both missed phone calls and those voicemails sitting in your iPhone Visual Voicemail.