The two big muscles found here are biceps and triceps, with brachialis sitting under the biceps. There are several nerves which run through to the hand and there can be referral pain from the neck as well as the shoulder itself and rotator cuff injuries.
Specific local pain in the upper arm, when you move or lift things, is likely to be muscle or tendon issues. The triceps can have issues like tendonitis, around the insertion point into the elbow, as can the biceps. This can be treated with a combination of shockwave, manual therapy and exercise.
Referred pain from the shoulder is a more constant ache when laying on the shoulder as well as when moving it. The rotator cuff in particular often refers deep into the upper arm and can cause confusion in diagnosis. This is treated by numerous methods, but the diagnosis needs to be correct to start with. Please see the shoulder section for this.
Neck issues refer a nervy, burning type pain to the upper arm, much like sciatica. This usually does not hurt to move the arm as such but builds up when at rest. Clearly, assessment and treatment of the neck are required which is described here. There is a lot that can be done though so don’t wait!
Fractures and muscle injuries caused by sports such as rugby are the most common things we see. Full ruptures of the biceps are not common but leave you with a ‘Popeye’ biceps. This is a nasty injury which can recover well if treated properly. One of the most famous in sports was Andrew Sheridan in the build-up to the 2011 Rugby World Cup.
The British Medical Journal in 2005 published an excellent review which can be found here.