Walnuts are an excellent source of antioxidants such as vitamin E (especially rich in gamma-tocopherol). They are a rich source of minerals like manganese, copper, potassium, calcium, iron, magnesium, zinc, phosphorus and selenium, and are also packed with many important B-complex vitamins like riboflavin, niacin, thiamin, pantothenic acid, vitamin B-6, and folates. 

Walnuts are the only nut significantly high in Omega-3s (specifically alpha-linolenic acid or ALA which is the plant-based omega-3 fatty acid). This is an essential fatty acid, meaning it's very much needed by the human body but not actually produced by the body itself. These healthy fats have been shown to help lower the risk of blood pressure, coronary artery disease, strokes and breast, colon and prostate cancers with their excellent anti-inflammatory action. An ounce of walnuts provides over 90% of the recommended daily intake of omega-3 fatty acids. 

Regular consumption of walnuts can also help lower total and LDL or "bad" cholesterol levels, all while promoting increases in HDL or "good" cholesterol levels.