Who came up with them: Japanese telecom companies. Back when doing their version of SMS, they found they had some room left over in the character set, so they included some little pictures you could send as if they were text characters. The Unicode Consortium included them in the Unicode standard, and Apple quietly included support for them in the iOS onscreen keyboard. They put it in there for Japanese users, but left it in for the rest of the world as well. And in the words of Tom Scott, some westerner found out "I can send piles of poo to my friends!"

This is why some of them are...slightly strange. "Levitating man in a suit" was some company's logo. The face that is exhaling clouds of steam is labeled "triumph" when in the west we associate that image with aggression, anger and frustration. It's why there's an emoji for "love hotel." Emoji have since been adopted worldwide and expanded...possibly excessively.