A "standard" SMS allows for most characters that you would typically use when writing a message. These are characters from the GSM 03.38 basic character set, and these messages are sent via 7-bit encoding.
If an SMS contains characters outside of the GSM basic character set, it will be converted and sent as unicode.

Unicode

Unicode characters are supported, but it's important to note that they reduce the character limit per message.*
The character limit for one unicode message is 70, or 67 characters each for multi-part messages.

* This is governed by mobile carriers, not ActivePipe.

Emojis

Yes, you can send emojis as part of an SMS*, however as they are outside of the GSM basic character set they are converted to unicode, and message character limits are reduced as described above. Emojis are counted as 2 unicode characters.

* If the recipients network does not support emoji, they will be stripped out.