Drift waves and drift vortices are low-frequency phenomena that occur in inhomogeneous plasmas embedded in strong magnetic fields. They propagate in the direction perpendicular to the density gradient and to the background magnetic field with phase velocities that are characterized by the diamagnetic velocity. Drift waves and vortices propagate in complementary velocity intervals. Most probably, they play an important role in the anomalous cross-field transport in magnetically confined plasmas. These phenomena can be described by a plasma model in which the electrons and ions are treated as separate fluids that are coupled through the electromagnetic field.