Bayesian phylogeography has been used in historical linguistics to reconstruct homelands and expansions of language families, but the reliability of these reconstructions has remained unclear. We contribute to this discussion with a simulation study where we distinguish two types of spatial processes: migration, where populations or languages leave one place for another, and expansion, where populations or languages gradually expand their territory. We simulate migration and expansion in two scenarios with varying degrees of spatial directional trends and evaluate the performance of state-of-the-art phylogeographic methods. Our results show that these methods fail to reconstruct migrations, but work surprisingly well on expansions, even under severe directional trends. We demonstrate that migrations and expansions have typical phylogenetic and spatial patterns, which in the one case inhibit and in the other facilitate phylogeographic reconstruction. Furthermore, we propose descriptive statistics to identify whether a real sample of languages, their relationship and spatial distribution, better fits a migration or an expansion scenario. Bringing together the results of the simulation study and theoretical arguments, we make recommendations for assessing the adequacy of phylogeographic models to reconstruct the spatial evolution of languages.