Spatial autocorrelation is an ubiquitous phenomenon in cross-sectional data that poses notable challenges for statistical inference. Even if indirect spillovers are not the main theoretical focus, unmodeled spatial dependence can cause common econometric methods to produce biased and inconsistent estimates. While political scientists so far predominantly rely on parametric spatial regression models, semiparametric spatial filtering techniques constitute a valuable alternative. By using the eigenfunction decomposition of a transformed connectivity matrix, the filtering approach generates a synthetic proxy variable from a linear combination of judiciously selected eigenvectors. Eigenvector selection is performed in a supervised or unsupervised fashion and different selection criteria can be specified. This synthetic variable acts as a surrogate for omitted spatial effects and removes spatial autocorrelation from the model residuals. This study introduces eigenvector-based spatial filtering to political science and discusses its strengths and weaknesses compared to parametric spatial models. Analytical results and Monte Carlo simulations show that spatial filtering resolves the bias due to neglected spatial dependence in non-spatial regression models. Overall, this study concludes that this semiparametric approach constitutes a very flexible and intuitive strategy that requires only a few assumptions. Given the widespread use of cross-sectional data, spatial filtering is applicable to a great variety of empirical analyses where spillovers are not the main quantity of interest. A new R package facilitates the application of this technique.