To the present date only the reconnection process for exactly antiparallel fields has been discussed in detail. In magnetospheric terms this restricts us to the consideration only of southward interplanetary fields. The qualitative study presented here shows how reconnection takes place between arbitrarily oriented fields in infinite and finite geometries. The process may best be thought of as a continuous exchange of field-line partners during the time a field line maps into the diffusion region. In a finite geometry the diffusion regions lie on field lines which connect neutral points of the field configuration, and along which a potential drop is imposed. Although the discussion here centers principally on the magnetosphere, the described reconnection process and field topology should also be applicable to other astrophysical problems.