This paper provides a comprehensive survey of asset pricing, emphasizing the interplay between theoretical models and empirical evidence, particularly focusing on the tradeoff between risk and return. The central concept is the stochastic discount factor (SDF), which prices all assets in the economy. The behavior of real interest rates and patterns of risk premia restrict the conditional mean and volatility of the SDF, respectively. The paper discusses various stylized facts about interest rates, stock prices, and stock returns, which have stimulated research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. The SDF is derived from the Arrow-Debreu model of general equilibrium, where a state price exists for each state of nature at each date, and asset prices are the weighted sum of future payoffs. The paper explores the theoretical and empirical aspects of the SDF, including its mean and variance, and the role of risk premia. It also examines the term structure of government bond yields and the multifactor models that have emerged from the literature. Empirical work on asset pricing often focuses on the predictability of asset returns, using historical data to estimate the SDF and test various models. The paper discusses the challenges and limitations of such empirical approaches, including small-sample biases and the "peso problem" (the possibility of unanticipated events affecting asset returns). The paper also reviews the literature on multifactor models, which attempt to explain the cross-sectional structure of stock returns. It discusses the Sharpe-Lintner Capital Asset Pricing Model (CAPM) and its deviations, known as "anomalies," such as the size effect, value effect, and momentum effect. These anomalies are often explained using multifactor models that include additional risk factors, such as human capital and distress risk. Finally, the paper addresses the problem of solving the present value relation for assets with multiple payoffs, discussing constant discount rates, rational bubbles, and loglinear approximate frameworks. It highlights the importance of understanding how the characteristics of payoffs determine asset prices and the stochastic properties of returns.This paper provides a comprehensive survey of asset pricing, emphasizing the interplay between theoretical models and empirical evidence, particularly focusing on the tradeoff between risk and return. The central concept is the stochastic discount factor (SDF), which prices all assets in the economy. The behavior of real interest rates and patterns of risk premia restrict the conditional mean and volatility of the SDF, respectively. The paper discusses various stylized facts about interest rates, stock prices, and stock returns, which have stimulated research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. The SDF is derived from the Arrow-Debreu model of general equilibrium, where a state price exists for each state of nature at each date, and asset prices are the weighted sum of future payoffs. The paper explores the theoretical and empirical aspects of the SDF, including its mean and variance, and the role of risk premia. It also examines the term structure of government bond yields and the multifactor models that have emerged from the literature. Empirical work on asset pricing often focuses on the predictability of asset returns, using historical data to estimate the SDF and test various models. The paper discusses the challenges and limitations of such empirical approaches, including small-sample biases and the "peso problem" (the possibility of unanticipated events affecting asset returns). The paper also reviews the literature on multifactor models, which attempt to explain the cross-sectional structure of stock returns. It discusses the Sharpe-Lintner Capital Asset Pricing Model (CAPM) and its deviations, known as "anomalies," such as the size effect, value effect, and momentum effect. These anomalies are often explained using multifactor models that include additional risk factors, such as human capital and distress risk. Finally, the paper addresses the problem of solving the present value relation for assets with multiple payoffs, discussing constant discount rates, rational bubbles, and loglinear approximate frameworks. It highlights the importance of understanding how the characteristics of payoffs determine asset prices and the stochastic properties of returns.