The exploration of cross-sectional data has been met with a renewed focus on methodological techniques to avoid the inferential errors associated with unaccounted spatial autocorrelation. Yet, political scientists have gone again and again to the same weathered tools in the spatial toolkit. This paper identifies spatial eigenfunction analysis (SEA)---particularly Moran eigenvector maps---as an underutilized tool that expands the spatial toolkit available to practitioners. SEA describes the relationship in spatial data based on (a combination of) eigenvectors which represent all possible map patterns at different spatial resolutions. Simulation exercises demonstrate that SEA offers multiple advantages for exploratory and inferential spatial analysis. First, it outperforms common approaches (such as Moran’s I) for identifying, visualizing, and simulating complex spatial patterns. Second, it facilitates the construction of a synthetic proxy variable that mimics the observed spatial structure to remove spatial dependence from model residuals. Finally, it partitions the proportion of explained variance in an outcome to the effects of covariates, space, and shared spatial structure. Thereby, it allows researchers to derive additional valuable insights from spatial data.