You can delete individual voicemails as you listen to them, and most networks will automatically delete old voicemails after 30 days. However, few networks offer a simple way of deleting multiple voicemail messages when your mailbox is full – unless you can use an option such as Visual Voicemail, which lets you delete messages with a quick tap of your finger.
3. If you don't have a voicemail already set up, "Default" will be checked. To set up your greeting, check "Custom."

Visual Voicemail is supported by most modern iPhones. However, the carriers themselves also have to support Visual Voicemail. Most major carriers do, but you’ll want to check with your carrier specifically to see if the feature is supported.
To set up Visual Voicemail, tap Set Up Now. You’ll be prompted to enter and confirm a voicemail password. Next, you’ll have the option to choose the default voicemail greeting or record your own. If you want to record your own custom greeting, tap Custom. Once you’ve entered created your password and chosen your greeting, you’ll be able to receive voicemails and view them in the Phone app.