We shall investigate some special aspects of vortex motion for some tarnsport models in fluid dynamics like  incompressible Euler equations. We shall mainly focus on  rotating  vortex patches which are concentrated vortices that do not change their shapes during the time and perform uniform rotation. We will analyze from analytical  point of view the  simply connected and doubly connected cases using techniques from complex analysis and bifurcation theory. Some numerical studies will be also discussed.