Many phenomenon of interest to social scientists exhibit some non-random spatial patterning. While the geographic distribution of variables can reveal valuable information about the underlying mechanisms, unaccounted spatial autocorrelation simultaneously causes severe problems for common econometric methods as it may lead to biased and inconsistent parameter estimates. In order to safeguard against false inferences and to utilize the spatial information contained in a variable, it is imperative for quantitative social scientists to apply appropriate techniques. To this end, this paper explores the utility of spatial eigenfunction analysis -- particularly Moran eigenvector maps (MEM) -- as a simple yet powerful tool for social scientists analyzing cross-sectional data structures. Based on the spectral decomposition of a transformed spatial connectivity matrix, this approach describes the spatial relationship in geo-referenced data based on eigenvectors which depict the full range of possible map patterns at different spatial resolutions. Simulation exercises demonstrate the utility and flexibility of spatial eigenfunctions for exploratory and inferential spatial analysis. More precisely, it facilitates the identification and visualization of multi-scale spatial patterns as well as the specification, estimation, and interpretation of inferential models involving spatial autocorrelation. This study concludes that spatial eigenfunction analysis broadens the spatial toolbox available to political scientists and allows practitioners to leverage the full range of statistical techniques suitable to appropriately analyze spatial data structures.