Geostrophic turbulence is a flow regime attained by turbulent, rotating, stably stratified fluids in near-geostrophic balance. When a small-scale forcing is present, flows in this regime may develop an inverse energy cascade. Geostrophic turbulence has been used in geophysical fluid dynamics as a relatively simple model of the large-scale planetary and terrestrial circulations. When the meridional variation of the Coriolis parameter (or a β-effect) is taken into account, the horizontal flow symmetry breaks down giving rise to the emergence of jet flows. In a certain parameter range, a new flow regime comes to life. Its main characteristics include strongly anisotropic kinetic energy spectrum and slowly evolving systems of alternating zonal jets. This regime is a subset of geostrophic turbulence and has been coined zonostrophic turbulence; it can develop both on a β-plane and on the surface of a rotating sphere. This regime was first discovered in computer simulations but later revealed in the laboratory experiments, in the deep terrestrial oceans, and on solar giant planets where it is believed to be the primary physical mechanism responsible for the generation and maintenance of the stable systems of alternating zonal jets. The hallmarks of zonostrophic turbulence are the anisotropic inverse energy cascade and complicated interaction between turbulence and Rossby–Haurwitz waves. Addressing the goals of the conference 'Turbulent Mixing and Beyond' that took place in August 2007 in Trieste, Italy, this paper exposes the regime of zonostrophic turbulence to a wide scientific community, provides a survey of this regime, elaborates its main characteristics, offers novel approaches to describe and understand this phenomenon, and discusses its applicability as a model of the large-scale planetary and terrestrial circulations.