Spatial/spatiotemporal interdependence—that is, that outcomes, actions or choices of some unit-times depend on those of other unit-times—is substantively important and empirically ubiquitous in binary outcomes of interest across the social sciences. Estimating and interpreting binary-outcome models that incorporate such spatial/spatiotemporal dynamics directly is difficult and rarely attempted, however. This article explains the inferential challenges posed by spatiotemporal interdependence in binary-outcome models and recent advances in their estimation. Monte Carlo simulations compare the performance of one of these consistent and asymptotically efficient methods (maximum simulated likelihood, using recursive importance sampling) to estimation strategies naïve about (inter-) dependence. Finally, it shows how to calculate, in terms of probabilities of outcomes, the estimated spatial/spatiotemporal effects of (and response paths to) hypotheticals of substantive interest. It illustrates with an application to civil war in Sub-Saharan Africa.