This monograph offers an overview of the active research area involving the class of PDEs known as Oskolkov equations. The author's analysis of these equations concentrates on thermal convection in a layer of incompressible fluid. Readers will learn how the Navier-Stokes equations, the Kelvin-Voigt equations, and the Navier-Stokes-Voigt equations are special cases of the generalized Oskolkov system. Thermal convection and double-diffusive convection are studied in Navier-Stokes-Voigt fluids and in various Kelvin-Voigt and Oskolkov fluids. Cutting edge research is included on magnetohydrodynamic convection in a Navier-Stokes-Voigt fluid and in a Kelvin-Voigt fluid of order one. Oskolkov Equations and Thermal Convection will serve as a timely resource for students and researchers interested in this active topic, as well as those studying the broader area of fluid dynamics.