A summary of recent research in the field of inverse design and optimization of coolant flow passages in the internally cooled configurations is presented. The methodology allows design engineers to prescribe desired surface temperature and heat flux distributions and to fix portions of the multiply connected realistically shaped configurations. The shapes of the resulting coolant flow passages can be arbitrarily or circularly shaped with a capability to maintain certain manufacturing geometric constraints. Unsteady cooling of organs and tissues in bioengineering is demonstrated by determining optimal time variation of thermal boundary conditions on the walls of the cooling container while maintaining the geometry and size of the configuration. Another concept suggests that components subjected to strong unsteady cooling or heating can be optimized for the desired time dependent overspecified surface thermal conditions by determining the corresponding instantaneous temperatures of the coolant flow passages. This effect can be achieved by applying optimal control of distributed coolant flow rates in each flow passage.