To send SMS and MMS messages in a Visual Basic .NET application using the Twilio API, first sign up for a Twilio account and obtain your Account SID and Auth Token. Purchase an SMS-capable phone number and download the Twilio .NET library. Using the library, create a new instance of the Message resource and specify the To, From, and Body parameters for your message. You can send messages to multiple recipients by creating an array of recipients and iterating through each phone number in that array. Additionally, you can send MMS messages by specifying a parameter for the URL of media, such as an image. The Twilio API provides a rate limit for sending messages, and you can check the capabilities of numbers in your account portal or query the Available Phone Numbers resource to search for Twilio numbers that are MMS enabled.