I'm a conservative cellular user. I keep cellular data off whenever I'm in range of WiFi, but also I keep WiFi off until I need it. This helps conserve battery life. I can usually go 3 days between charges.
When I get an MMS message, or multi-person message, my HTC 10 (Android) will notify me of the message and as "not downloaded". I turn on cellular or WiFi and then download. No problem. Works fine.
However, I've had a very strange problem with text messaging from a specific family member who has an iPhone. Sometimes her text messages are NOT received by me. AND... sometimes she is not getting my text messages. It happens very infrequently. And when it does happen, it's when we're in "message tag," meaning we're not in an active back-and-forth stream of texting.
In my case, I'm not sending any multi-media. If I send an emoticon, I usually use ASCII ones, so 160 chars is the message limit (special emoticons reduce message to 70 chars).