We examine world migration as a social-spatial network of countries connected via movements of people. We assess how multilateral migratory relationships at global, regional, and local scales coexist ("glocalization"), divide ("polarization"), or form an interconnected global system ("globalization"). To do this, we decompose the world migration network (WMN) into communities---sets of countries with denser than expected migration connections---and characterize their pattern of local (i.e., intracommunity) and global (i.e., intercommunity) connectivity. We distinguish community signatures---"cave", "biregional", and "bridging"---with distinct migration patterns, spatial network structures, temporal dynamics, and underlying antecedents. Cave communities are tightly-knit, enduring structures that tend to channel local migration between contiguous countries; biregional communities are likely to merge migration between two distinct geographic regions (e.g., North Africa and Europe); and bridging communities have hub-and-spoke structures that tend to emerge dynamically from globe-spanning movements. We find that world migration is neither globally interconnected nor reproduces the geographic boundaries as drawn on a world map but involves a heterogeneous interplay of global and local tendencies in different network regions. We discuss the implications of our results for the understating of variability in today's transnational mobility patterns and migration opportunities across the globe.