In general since the heart is a muscle it is not considered a radio-sensitive structure. Nevertheless radiation can cause damage to the heart muscle (carditis) to the wrapper or pericardium (pericariditis) and to the coronary arteries (increase the risk of a heart attack or myocardial infarction (see here and here). See dose limites from the RTOG (9311 and 0412).
There are radiation dose limits (go here) and dose limit
guidelines (see here.) In
patients who have received high doses of a drug that can effect the heart (like
Adriamycin) it is even more important to limit the dose of radiation that hits the heart
muscle (left ventricle).
In women with breast cancer the old radiation technicques hit the heart and the risk of a heart attck was increase. With modern techniques this is no longer a problem (see here and here).
occasionally radiation to the heart can inflame the pericardium and cause problems with restriction, in the CT scan shown above, breast cancer spread to the pericardium causing a large fluid collection around the heart restricting heart function (called tamponade)