This paper shows that belief differences have strong effects on asset prices in consumption-based asset-pricing models with long-run risks. Belief heterogeneity leads to time-varying consumption and wealth shares of the agents. This time variation can resolve several asset-pricing puzzles, including the large countercyclical variation of expected risk premia, the volatility of the price-dividend ratio, the predictability of cash flows and returns, and the large predictability of returns in recessions. These findings show that belief differences, a widely observed attribute of investors, significantly improve the explanatory power of long-run risk asset-pricing models.