Hey Alison,
I think that depends a little bit on the SMS provider you are using. For example, if you use Twilio you would need to use USC-2 encoding. Also, as far as I know not every phone can display every emoji since there are different databases of them, e.g. Apple, Samsung, Windows etc.
Hope that helps,
Felix
Hi @Alison! One more comment to this one - emojis are not part of the 7bit encoding, that is used as a standard for the SMS. Therefore, any emoji in the SMS text will cut its length from 160 characters down to just 70 characters. As the result, it can double or even triple the SMS cost easily, if you are not aware of this and keep the message 160 characters long.
Thank you Felix and Kriss for your answers, it helps me a lot !