According to the Milankovitch theory, the changes in the Earth's orbit induce variations of the insolation received on the Earth's surface that have an impact on large climatic changes. So a precise astronomical solution of the Earth's motion is needed for paleoclimate studies. At present, the most advanced Earth orbital and rotational solutions for long time span are the La2004, La2010, La2011 solutions, which have been obtained by direct numerical integrations of the planet orbits and the equations of the Earth's rotation theory. These solutions have been used for age calibration of geological data over more than 50Ma in the past. Due to chaotic behavior, the precision of the solutions decreases rapidly beyond this time span. In this paper, we give an overview about these solutions and present the development status and trends of the orbital and rotational evolution of the Earth. The details about the numerical integrations of the long term motion of the Solar System are given in the Chapter 2. Chapter 3 mainly introduces the long-term precession of the Earth. The following chapter is focussed on the long term cycles in its evolution. Chapter 5 mainly describes the stability of the numerical solutions and the Solar System. Finally, a discussion and proposal for future study is made.