The solar wind and its embedded magnetic field, the interplanetary magnetic field (IMF) together with magnetic reconnection power the large-scale plasma and magnetic flux circulation in the Earth's magnetosphere-ionosphere system. This circulation is termed as convection and its strength is controlled by the north-south IMF component (IMF Bz). In recent years, an interest has arisen to investigate the lesser-known role of the dusk-dawn component (IMF By) in convection. It has been previously known though that prevailing nonzero IMF By can cause plasma flow asymmetries in the high-latitude ionosphere, but how the magnetospheric flows, for instance, in the magnetotail plasma sheet are affected, remains to be investigated. In this article, we introduce the recent progress and the latest achievements in the research of the influence of IMF By on tail plasma sheet convection. The research progress has been rapid and it has revealed that both fast and slow convection are affected in a manner that is in accordance with the asymmetries observed in the ionospheric convection. The results indicate the significance of the IMF By component on magnetospheric convection and they represent a major advance in the field of solar wind-magnetosphere coupling.