Actually, since MMS is an old thing since 2G. I should say, better to refer to OMA stardard for the latest information. (Multimedia Messaging Service
Architecture Overview)

MMS is pretty simple, you only need a phone with PS connection (3G or GPRS) and then you send the mms content (PDU) to the MMSC via HTTP using a proxy as WAP Gateway (convert HTTP to WSP). MMSC proxy would also do user authenication so that not everyone can send or retrieve message from everyone.

Of course, the conversion of HTTP to WSP won't be needed if your phone is using WAP stack instead of TCP connection to server.

Apart from the Proxy and the MMSC, which stores and forwards MMS messages from one to other users, there we rely on SMSC or a push gateway to send notification to users. Hence the notification could either be sent via SMS or IP push messages.

Moreover, MMS should be sent to Email user. Therefore MMS itself is sent from handset to MMSC and MMSC does forward MMS to Email server via SMTP.