Over the past thirty years, the generative framework has greatly contributed to the study of both the internal and external syntax of spatial adpositions, with the intent—among many other things—of giving a unitary account of their heterogeneous nature and behavior. Once the Cinderellas of grammar, prepositions have been extensively investigated in earlier research. The major result of these studies was to show that prepositional phrases have a complex internal structure, and that the grammatical encoding of locative meaning has its own place in UG. This volume constitutes the implementation and the ideal continuation of the seminal proposals in the generative tradition. The essays collected in the first part of the volume not only test these proposals against new (micro-)comparative data, but also shed new light on the relation between spatial expressions and other semantic relations like possession. The second part of the volume looks beyond spatial PPs, exploring the role of Ps not only in non-spatial environments such as comitatives, but also in more general phenomena like verbal affixation, ellipsis, and complementation.