All science is the search for unity in hidden likeness (Bronowski, 1988). There are two practical reasons to approximate processes that produce such hidden likeness: (1) prediction for interpolation or extrapolation to unknown (often future) situations; and (2) inferenceto understand how variables are connected or how change in one affects others. Statistical learning tools aid prediction and at times inference. In recent years, rapidly growing computing power, the advent of machine learning algorithms, and more user-friendly programming languages (e.g., R and Python) support applying statistical learning methods to broader societal problems. This dissertation develops statistical learning models, generally simpler than mechanistic models, to predict unimpaired flows of California basins from available data. Unimpaired flow is the flow produced by the basin in its current state, but without human-created or operated water storage, diversion, or return flows (California Department of Water Resources, Bay-Delta Office, 2016). The models predict unimpaired flows for ungauged basins, an International Association of Hydrological Sciences "grand challenge" in hydrology. In Predicting Ungauged Basins (PUB), the models learn from information at gauged points on a river and extrapolate to ungauged locations. Several issues arise in this prediction problem: (1) How we view hydrology and how we define observational units determine how data is pre-processed for statistical learning methods. So, one issue is in deciding the organization of the data (e.g., aggregate vs. incrementalbasins). Such data transformation or pre-processing is explored in Chapter 2. (2) Often, water resources problems are not concerned with accurately predicting the expectation (or mean) of a distribution but require better estimates of extreme values of the distribution(e.g., floods and droughts). Solving this problem involves defining asymmetric loss functions, which is presented in Chapter 3. (3) Hydrologic observations have inherent dependencies and correlation structure; gauge data are structured in time and space, and rivers form a network of flows that feed into one another (i.e., temporal, spatial, and hierarchical autocorrelation). These characteristics require careful construction of resampling techniques for model error estimation, which is discussed in Chapter 4. (4) Non-stationarity due to climate change may require adjustments to statistical models, especially for long-term decision-making. Chapter 5 compares unimpaired flow predictions from a statistical model that uses climate variables representing future hydrology to projections from climate models. These issues make Predicting Ungauged Basins (PUB) a non-trivial problem for statistical learning methods operating with no a priori knowledge of the system. Compared to physical or semi-physical models, statistical learning models learn from the data itself, withno assumptions on underlying processes. Their advantages lie in their fast and easy development, simplicity of use, lesser data requirements, good performance, and flexibility in model structure and parameter specifications. In the past two decades, more sophisticated statistical learning models have been applied to rainfall-runoff modeling. However, with these methods, there are issues such as the danger of overfitting, their lack of justification outside the range of underlying data sets, complexity in model structure, and limitations from the nature of the algorithms deployed. Keywords: predicting ungauged basins (PUB); rainfall-runoff modeling; asymmetric loss functions; structured data; blocked resampling methods; climate change; water resources; hydrology; statistical learning.