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This dissertation advances statistical methodology en route to providing new solutions to major questions in empirical finance. The common theme is the balance between structure and flexibility in these models. I show that structure, while it is potentially statistical bias, improves model performance when wisely chosen. Specifically, I look at asset returns' behavior: their relationship with firm characteristics, how they change over time, and what elements may cause their behavior. First, I investigate the forecasting of multiple risk premia. Using the content of Fisher et al. (2019a), I introduce a simulation-free method to model and forecast multiple asset returns and employ it to investigate the optimal ensemble of features to include when jointly predicting monthly stock and bond excess returns. This approach builds on the Bayesian Dynamic Linear Models of West and Harrison (1997), and it can objectively determine, through a fully automated procedure, both the optimal set of regressors to include in the predictive system and the degree to which the model coefficients, volatilities, and covariances should vary over time. When applied to a portfolio of five stock and bond returns, I find that my method leads to large forecast gains, both in statistical and economic terms. In particular, I find that relative to a standard no-predictability benchmark, the optimal combination of predictors, stochastic volatility, and time-varying covariances increases the annualized certainty equivalent returns of a leverage-constrained power utility investor by more than 500 basis points. Here, linear structure is chosen, and then I analyze what parameters should be flexible over time. Second, I consider the problem of determining which characteristics of a firm impact its stock returns. Using the content of Fisher et al. (2019b), I first model a firm's expected return as a nonlinear, nonparametric function of its observable characteristics. I investigate whether theoretically-motivated monotonicity constraints on characteristics and nonstationarity of the conditional expectation function provide statistical and economic benefit. Then, using this model, I provide an approach for characteristic selection using utility functions to summarize the posterior distribution. Standard unexplained volume, short-term reversal, size, and variants of momentum are found to be significant characteristics, and there is evidence that this set changes in time. The data also provide strong support for monotonicity in some of the characteristics' relationships with returns. Hence, the flexibility of the nonlinear, nonparametric curves are regulated by monotonic constraints. Finally, I turn to causal inference to ask which of these characteristics have causal relationships with asset returns. Hahn et al. (2018b) allow for regularized estimation of heterogeneous effects, and I modify their work to allow for non-binary, continuous treatments. This method is highly flexible at fitting complicated response surfaces with discontinuities, interactions, and nonlinearities, and thus benefits from added structure in the form of regularization from shrinkage priors. I demonstrate the model's ability to show the effect of firm size on returns, while controlling for book-to-market.