Microchannels with curved geometries have been employed for many applications in microfluidic devices in the past decades. The Dean vortices generated in such geometries have been manipulated using different methods to enhance the performance of devices in applications such as mixing, droplet sorting, and particle/cell separation. Understanding the effect of the manipulation method on the Dean vortices in different geometries can provide crucial information to be employed in designing high-efficiency microfluidic devices. In this review, the physics of Dean vortices and the affecting parameters are summarized. Various Dean number calculation methods are collected and represented to minimize the misinterpretation of published information due to the lack of a unified defining formula for the Dean dimensionless number. Consequently, all Dean number values reported in the references are recalculated to the most common method to facilitate comprehension of the phenomena. Based on the converted information gathered from previous numerical and experimental studies, it is concluded that the length of the channel and the channel pathline, e.g., spiral, serpentine, or helix, also affect the flow state. This review also provides a detailed summery on the effect of other geometric parameters, such as cross-section shape, aspect ratio, and radius of curvature, on the Dean vortices’ number and arrangement. Finally, considering the importance of droplet microfluidics, the effect of curved geometry on the shape, trajectory, and internal flow organization of the droplets passing through a curved channel has been reviewed.