What proof is there that CBD is effective? Is there research?

There are a large number of both animal and human trials studying the mechanisms and benefits of CBD. While these trials cover the potential treatment of a wide scope of conditions, there are not many full-scale clinical trials, therefore these indications are clearly just that for now. 

GW pharmaceuticals have recently secured a marketing authorisation for a CBD based product called Epidiolex, for the treatment of Dravets Syndrome, a rare and severe form of epilepsy in children.