Every day the news reminds us that we live in a complex, ever-changing world. Against that background, this dissertation studies the econometrics of the interaction between time-varying uncertainty and learning. In particular, it develops parsimonious nonparametric methods for estimating risk in real time. The first two chapters develop tractable models and estimators for entire densities. The third chapter provides identification-robust inference for the prices of market and volatility risk when volatility exhibits complex dynamics. The first chapter, "Jumps, Realized Densities, and News Premia," studies how jumps affect asset prices. It derives both a tractable nonparametric continuous-time representation for the price jumps and an implied sufficient statistic for their dynamics. This statistic — jump volatility — is the instantaneous variance of the jump part and measures news risk. It also develops estimators for the volatilities and nonparametrically identifies continuous-time jump dynamics and associated risk premia. It also provides a detailed empirical application to the S&P 500, showing that the jump volatility commands a smaller premium than the diffusion volatility does. The second chapter, "Bypassing the Curse of Dimensionality: Feasible Multivariate Density Estimation," is coauthored with Minsu Chang and studies nonparametrically estimating multivariate densities. Most economic data are multivariate and estimating their densities is a classic problem. However, the curse of dimensionality makes nonparametrically estimating the data’s density infeasible when there are many series. This chapter does not seek to provide estimators that perform well all of the time (it is impossible) but instead adapts ideas from the Bayesian compression literature to provide estimators that perform well most of the time. The third chapter, "Identification-Robust Inference for Risk Prices in Structural Stochastic Volatility Models," is coauthored with Xu Cheng and Eric Renault and studies the identification problems inherent to measuring compensation for risk in stochastic volatility asset pricing models. Disentangling the channels by which risk affects expected returns is difficult and poses a subtle identification problem that invalidates standard inference. We adapt the conditional quasi-likelihood ratio test Andrews and Mikusheva (2016) develop in a GMM framework to a minimum distance framework to provide uniformly valid confidence sets.