The muscles between the elbow and wrist are the Forearms. Forearms include four main muscle groups: Forearm Flexors, Wrist Flexors, Extensor Muscles and Brachioradialis. The front part of the forearm consists of brachioradialis and extensors muscles which help you to extend and move the back of your hand towards your forearm. The inner part of your forearm consists of flexor muscles, their duty is to flex and move your palm towards your forearm and to move your fingers. Forearm muscles give you most of your grip strength .
Forearm exercises are pretty straight forward to do. Every time you exercise your forearms, especially in the beginning, it should really feel on your forearms muscles. If the exercising doesn't make your forearms to work, something is going wrong. Again, the motion is the key not the weights, as you progress you can add weights when the exercises start to feel too easy, but make sure the motion remains clean.