What is vedanā?

Vedanā is usually translated as "feeling" or "sensation". In S.N. Goenka's tradition, vedanā is understood as a physical sensation on the body, such as touch, heat, pain, etc. As far as I understand, vedanā does not include other senses, such as taste, smell, sound or sight (even though vedanā may arise as a result of perception of something through these senses). Nor are mental feelings such as anger, hatred or joy classified as vedanā. Do I understand it correctly? How is vedanā defined in other traditions? Are there any significant differences?