In this paper, present status of super high-efficiency tandem solar cells has been reviewed and key issues for realizing super high-efficiency have also been discussed. In addition, the terretrial R&D activities of tandem cells, in the New Sunshine Program of MITI(Ministry of International Trade and Industry) and NEDO(New Energy and Industrial Technology Development Organization) in Japan are reviewed briefly. The mechanical stacked 3-junction cells of monolithically grown InGaP/GaAs 2-junction cells and InGaAs cells have reached the highest efficiency achieved in Japan of 33.3% at 1-sun AM1.5. This paper also reports high-efficiency InGaP/GaAs 2-junction solar cells with a world-record efficiency of 26.9% at AM0, 28$^{circ}C$ and radiation damage recovery phenomena of the tandem cell performance due to minority-carrier injection under light illumination or forward bias, which causes defect annealing in InGaP top cells. Future prospects for realizing super-high efficiency and low-cost tandem solar cells are also described.