Robot path planning is a typical example of a problem that requires searching a “continuous” space, the robot's configuration space, for a solution, a collision-free path. The global approach to path planning first captures the connectivity of the robot's free space into a concise connectivity path, and next searches this graph. The local approach directly embarks on a search procedure, and performs geometric computation according to the needs of the search. Global methods may waste a large amount of computation before they have any chance to find a path. On the other hand, local methods, which lack the global vision provided by the connectivity graph, have very poor worst-case complexity. Is it possible to instill some local opportunism in a global approach, or a limited amount of precomputed global information in a local approach? More generally: How can geometric computation and search help each other to produce a path quickly? These questions probably do not have definite domain-independent answers. However, raising them may help us engineer path planners that better meet specific application needs. This paper considers these questions through a series of informal case studies, each corresponding to a particular way to engineer the interaction between geometry and search in a path planner.