Kybella has been used for many years. It used to be called mesotherapy, but back then no product was tested or controlled by the FDA. In recent years, a company called Kythera manufactured a compound to destroy fat, which gained an FDA clearance in 2015, called Kybella.
A short amount of time after that, Allergan, the cosmeceutical giant, purchased Kythera and their product Kybella, and dropped the Kythera name.
Since then, this product has been gaining widespread popularity.