(abstract pending)We model the role of attention in decision making under risk and uncertainty from the perspective of the decision maker as a cognitive miser, and arrive at the utility of a lottery through potentially volatile attention-dependent decision weights. The resulting Attention Theory (AT) can account for a broad range of choice phenomena in the literature under different attentional attitudes. Under consequentialist attention, AT exhibits continuity in decision weights and can account for Allais behavior, fourfold pattern of risk attitude, and disjunction effect. Under a weaker form of consequentialist attention which accommodates a variable attention function, AT can exhibit ambiguity aversion, discontinuity in valuation from event splitting, and uncertainty effects. When bottom-up salience is significant, AT delivers source dependence, heterogeneity in gain-loss attitude, and stochastic choice from excessive inattention when bottom-up salience is random. In binary choice, AT yields a class of correlation preference which overlaps substantially with regret theory (top-down), and reduces to salience theory (bottom-up) when the bivariate attention function is symmetric.