When the dawn‐to‐dusk component of the interplanetary magnetic field (IMF BY) is dominant, ionospheric convection exhibits a distorted two‐cell pattern with its dawn‐dusk and interhemispheric asymmetries regulated by the IMF BY polarity. For BY > 0, the convection in the Northern (Southern) Hemisphere usually consists of a relatively round cell on the duskside (dawnside) and a crescent‐shaped cell on the dawnside (duskside); for BY < 0, the dawn‐dusk relationship is reversed. However, deviations from the basic round/crescent cell pattern are sometimes seen. Such nonstandard convection patterns include the dayside‐enhanced crescent cell pattern, nightside‐enhanced crescent cell pattern, split crescent cell pattern, and exchange cell pattern. Although at times the nonstandard convection patterns appear to be quite different from the basic round/crescent cell pattern, the underlying physical processes (i.e., the types of reconnection) and field line topologies are basically the same. We show that these various convection patterns can be synthesized by considering the topologies of magnetic field lines involved in eight types of reconnection. We also discuss the formation mechanism of the theta aurora configuration in terms of magnetic topology and ionospheric convection. The theta aurora configuration results from transient reconnection‐driven convection when an IMF BY polarity switch reconfigures the exchange cell pattern. The bifurcation of the polar cap occurs as a consequence of accumulation of closed magnetic flux in the sunward return flow region of the round cell and intrusion of open magnetic flux into the “sub polar cap” that had been established by the primary exchange cell prior to the IMF change.