Although they account for most of the important applications of gas-solid fluidization, the turbulent fluidization and dense suspension upflow (DSU) regimes have received far less attention than less important gas-solid flow regimes like bubbling and fast fluidization. This has arisen for various historical and practical reasons, but it is important that the balance now be redressed. The term turbulent fluidization covers two different types of transitional behaviour for voidages of approximately 0.65 to 0.8, one following a relatively sharp breakdown of bubbling and the other involving intermittency. The DSU regime has only recently been identified as being distinct from turbulent and fast fluidization. even though it has been applied extensively in fluid catalytic cracking for many yeats. Early approaches to the study and modelling of these two flow regimes tend to be empirical or oversimplified. More promising approaches are now under development based on a statistical probability approach, dissipative structures and computational fluid dynamics (CFD). The difficulties and prospects are discussed in this paper. Such features as turbulence, energy dissipation, intermittency, chaos and computational modelling need to be studied to improve the mechanistic understanding of these flow regimes.