I have re-examined old records of the theories of heavenly structure, especially Gaitian蓋天 and Huntian渾天 theory. The following are the basic points of my findings. First of all, the first meaningful Chinese explanation on the structure of heaven begins with the Gaitian, Huntian, and Xuanye宣夜 theories which appeared in the Han period. Some insisted that Tianyuandifang天圓地方 is the oldest Chinese explanation, but I think it is too vague a description. Secondly, it is generally accepted that Gaitian theory is divided into two: the first and the second Gaitian theories. That division was suggested by Noda Churyo能田忠亮 in 1933, but I do not agree to Noda's division because it has no concrete evidence and did not help us to understand the theory better. In addition, there were at least two different schools of the Gaitian theory: One is found in Zhoubisuanjing周髀算經, and the other is suggested by the Zhoubi experts周髀家. Thirdly, Huntian theory, which is organized by Zhang Heng 張衡, is different from Gaitian theory in the way it describes the relationship between the heaven and the earth. Gaitian theory explained the structure of the two as being "above" and "below". On the other hand, Huntian theory described them as being "inside" and "outside" -- the heaven embracing the earth. And the shape of the earth is not a serious matter in this theory. Fourthly, there were severe debate between the two schools, but they did not focus themselves on the main issue of the heavenly structure. Finally, most scholars agreed that Chinese astronomy was very practical and computational. But the acient Chinese cosmology was very theoretical and speculative. And furthermore, Chinese had a lot of diversities and flexibility in their cosmological thinking.