The planetary background rotation and density stratification play an essential role in the dynamics of most large-scale geophysical vortices. In this chapter we will discuss some basic dynamical aspects of rotation and stratification, while focusing on elementary vortex structures. Rotation effects will be discussed in Sect. 1.1, attention being given to basic balances, Ekman-layer effects, topography and ß-plane effects, and vortex instability. Some laboratory experiments will be discussed in order to illustrate the theoretical issues. Section 1.2 is devoted to vortex structures in stratified fluids, with focus on theoretical models describing their decay. Again, laboratory experiments will play a central part in the discussion. Finally, some general conclusions will be drawn in Sect. 1.3. For additional aspects of the laboratory modelling of geophysical vortices the interested reader is referred to the review papers  and .