This paper presents an overview of the numerical simulation studies to date, of vertical vortices, or dust devil--like vortices, which arise in atmospheric convective boundary layers (CBLs). The similarities and differences between these studies are highlighted. In addition, the accuracy of the simulated vortices as compared with observed physical characteristics is discussed. It is notable that vertical vortices formed in all of the studies considered for both Mars and Earth simulations, despite the fact that they have not often been pointed out in laboratory and numerical simulations of CBLs. A possible implication of this finding is that non-visible vertical vortices may even be ubiquitous and thus may play an important role in boundary layer transports. If this is so, they may have implications for pollution and hazardous waste transports, as well as on impacts on descent and landing of spacecraft on Mars.