This lecture is will describe a research program directed at uncovering the cognitive mechanisms involved in non-expert understanding and use of information to make decisions under uncertainty. It will begin by providing background on the key principles of human information processing, including its strengths and limitations, that form the basis of the cognitive approach. Then it will focus on issues related to decision-making under uncertainty, from an applied perspective, in the context of weather and climate. Primary among these is the impact of communication format on decision-makers understanding, trust and choices. Evidence will be provided from experiments supporting the claim that non-experts can understand and make good use of numeric likelihood information (e.g. 30% chance of rain) regardless of educational background. However, this evidence also suggests that understanding is practical rather than theoretical. In the second part of the talk, cognitive issues related to understanding and attitudes toward climate change will be discussed. This section will describe experimental evidence that addresses the impact of climate communication strategies on motivation as well as their relationship to political ideology. The results of both approaches suggest that non-experts can understand and make good use of scientific information if it is presented in a way that takes into account human information processing characteristics and prior knowledge.