The results obtained by using finite time thermodynamics (FTT) are universal and have become one of important foundations of thermo-physics. A large number of researches have been carried out in the performance optimizations and optimal configurations of single-and multi-stage two-heat-reservoir direct and inverse thermodynamic cycles by using FTT. The obtained new results have more important practical significance for engineering design and optimization than those obtained by using classical thermodynamics. This paper reviews the new advances of the optimal performances and optimal configurations of single and multi-stage two-heat-reservoir direct and inverse thermodynamic cycles following different heat transfer laws, including the new advances of the optimal performances of endoreversible and irreversible Carnot heat engine, Carnot refrigerator and Carnot heat pump cycles under different heat transfer laws, and the new advances of the optimal configurations of two-heat-reservoir heat engine, refrigerator and heat pump cycles, as well as multi-stage complex thermodynamic cycles with different heat transfer laws.