To illustrate the basic features of magnetospheric topology, the development of a global model is traced from the superposition of dipole and uniform fields to the effects of adding, in turn, diffusion regions, surface currents and a magnetic field component normal to the magnetopause. The subsolar, antiparallel, tearing and patchy merging geometries proposed in the past all emerge under various conditions, but models that deduce merging geometry from global boundary conditions are lacking. An exception is a model in which the external field merges wherever it falls tangent to the magnetopause. The result is a subsolar merging line that has all the characteristics of early sketches based on local arguments. Magnetosheath plasma beta affects magnetospheric topology and, consequently, merging geometry. Low, high and variable beta favor subsolar, tearing and patchy merging, respectively. Proposed flux transfer event models of bursty reconnection from a single merging line, flux ropes from multiple merging lines and flux tube elbows from patches can also be categorized by plasma beta in the same respective order. The topological modeling reviewed here may prove to be most useful for interpreting merging results from MHD simulations.