Based on analysis of paleoclimate data for the Pleistocene and the Phanerozoic as a whole, this paper advances a new concept of the orbital astronomical theory of paleoclimate. The need for a new concept is shown to be necessitated by two circumstances. The first is the grave disagreement between the M.Milankovitch theory and empirical data. The second is the considerable drawbacks of this theory, which is currently viewed as being analogous to the astronomical theory of paleoclimate. In particular, the paper shows that the insolation curves calculated by Milankovitch for individual latitudes and caloric half-years not to mention months or even days, as in the works of Milankovitch's followers have no global paleoclimatic significance and cannot be used in paleoclimate reconstructions or modeling. Notions developed in the framework of the new concept provide a systematic basis on which to explain the singularities of climate changes coupled to orbital periodicities during the different geologic eras of the Phanerozoic. For example, proposed is a systematic approach to solving the issues of the 100-ka climatic periodicity of the Pleistocene, the mid-Pleistocene transition, and the lack of the 400-ka climatic periodicity within the last two million years.