My dissertation is developed to address unresolved issues in the asset pricing literature, focusing on both risk premium levels and dynamics. Chapter 1 addresses short-horizon risk premium dynamics. In the data, stock market volatility weakly or even negatively predicts short-run equity and variance risk premia, challenging positive risk-return trade-offs at the heart of leading asset pricing models. I show that a puzzling negative volatility-risk premia relationship concentrates in scattered high-uncertainty states, which occur about 20\% of the time. While at other times, the relationship is strongly positive. I develop a micro-founded learning model in which due to learning frictions investors underreact to structural breaks in high-volatility periods and overreact to transitory variance shocks in normal times. The model can successfully explain the novel time-varying volatility-risk premia relationship at short and long horizons. The model can further account for many other data features, such as a robust positive correlation between equity and variance risk premium, the leverage effect, and negative observations of equity and variance risk premia at the onsets of recessions. Chapter 2, coauthored with Professor Bjorn Eraker, focuse on equilibrium derivatives pricing. It is motivated by the observation that leading asset pricing models typically can not explain the levels or dynamics of VIX options prices. We develop a tractable equilibrium pricing model to explain observed characteristics in equity returns, VIX futures, S\&P 500 options, and VIX options data based on affine jump-diffusive state dynamics and representative agents endowed with Duffie-Epstein recursive preferences. A specific model aimed at capturing VIX options prices and other asset market data is shown to successfully replicate the salient features of consumption, dividends, and asset market data, including the first two moments of VIX futures returns, the average implied volatilities in SPX and VIX options, and first and higher-order moments of VIX options returns. In the data, we document a time variation in the shape of VIX option implied volatility and a time-varying hedging relationship between VIX and SPX options which our model both captures. Our model also matches many other asset pricing moments such as equity premia, variance risk premia, risk-free interest rates, and short-horizon return predictability. To derive our specific model, we first develop a general framework for pricing assets under recursive Duffie-Epstein preferences with IES set to one under the assumption that state variables follow affine jump diffusions, as in \citet{DPS00}. Relative to the literature, our framework has a clear marginal contribution that it is an endowment-based equilibrium model with (i) clearly stated affine state variable dynamics and (ii) precisely characterized equilibrium value function, risk-free rate, prices of risks, and risk-neutral state dynamics. We prove our state-price density is a precise $IES\to1$ limit of that approximately solved in \citet{ErakShal08}. The recursive preference assumption implies that higher-order conditional moments of the economic fundamental, such as its growth volatility and volatility-of-volatility, are explicitly priced in equilibrium. Since VIX derivatives depend on these factors, this in turn implies that the former carry non-zero risk premia.