The Rossby wave instability has been proposed as a mechanism to transport angular momentum in the dead zone of protoplanetary disks and to form vortices. These vortices are of particular interest to concentrate solids in their centres and eventually to form planetesimals. Here we summarize some recent results concerning the growth and structure of this instability in radially and vertically stratified disks, its saturation and non-linear evolution. We also discuss the concentration of solids in the Rossby vortices including vertical settling