Six illustrations are given of the use of single-particle theories with elastic dumbbells and other simple models in polymer kinetic theory: (1) Marrucci's incorporation of thermal history in rheological equations of state; (2) Radial migration of polymers in a coaxial-cylinder viscometer (Uhlenhopp effect); (3) Crude incorporation of excluded volume effects; (4) Finite extensibility effects and the use of Peterlin's approximation; (5) Use of the Wang—Zimm theory to describe concentration effects in the non-Newtonian viscosity of solutions; and(6) Hydrodynamic interaction and the “effective velocity gradient” approximation. The dumbbell kinetic theory results have supplied useful guidance in the rheology and fluid dynamics of polymers.