You'll want to sign up for Visual Voicemail (VVM) in order to start checking them online. Once you've successfully done that, you can start managing/downloading your voicemails online and in the application on Androids.
If you're the Primary Account Holder, you can review and manage your messages using your computer:
Go to My T-Mobile and log in to your account.
Click PHONE at the top of the page.
In the list along the right, click Check Voicemail.
On the new page that opens, you have several options:
Listen to a message: Click the play button just to the left of the message.
Take action on a message: Simply check the box to the far left of one or more of the messages. Once a message is checked, you can delete, mark as unread, download, etc.
Forward a message to an email address: Click Send as email to the far right of a message, add the email recipient in the To box, and then click Send e-mail.