Risk communications are frequently intended to help people understand hazards they face, with the hope that this understanding will help them make better decisions about the need for action or help them choose among alternative actions. To evaluate the success of such communications, a definition of "understanding" is needed. This paper suggests that decisions about personal risks require, at a minimum, information about the nature and likelihood of potential ill effects, information about the risk factors that modify one's susceptibility, and information about the ease or difficulty of avoiding harm. Even if these attributes are accepted as essential criteria for understanding, research on risk perceptions suggests that assessing what people know or believe is sometimes quite difficult. The focus of the paper is on the several dimensions of risk comprehension. Examples of how each can be assessed are drawn from research on public perceptions of the risks from smoking. These examples demonstrate that the public has only a limited understanding of smoking risks.