Diamond has a series of extreme characteristics superior to other materials, and also very wide application scope. The large diamond single crystal can play a role in its functional characteristics, which has become a research hotspot. In this paper, we introduce the principle and process of synthesizing large diamond single crystal by temperature gradient method (TGM) under high pressure and high temperature (HPHT), and summarizes the research status and research directions of different types of and additives-doped large diamond single crystals respectively. The principle of the temperature gradient method is that the carbon source, driven by the temperature gradient, diffuses from the high concentration region at the high temperature end to the low concentration region at the low temperature end, and diamonds are grown on the seed crystal. The growth rate of diamond crystal is controlled by adjusting the axial temperature gradient at synthesis cell, and the shape growth of Ib-type large diamond is controlled by the distribution in the V-shaped growth area. We introduce different kinds of diamond large single crystals from five aspects. Firstly, the Ia-type diamond large single crystal can be obtained by the annealing treatment of Ib-type diamond under HPHT. The conversion rate of C centre to A centre for nitrogen in diamond is improved by optimizing the conditions of HPHT. Secondly, the Ib-type larger diamond is studied very much in the following areas: the analysis of its surface characteristic, the control of inclusions and cracks, the precipitation mechanism and the elimination measures of regrown graphite and the mass production technology of multiseed method. Thirdly, IIa-type large diamond single crystal is introduced in which the nitrogen getter is selected due to the ability Al and Ti (Cu) to getter nitrogen, the catalyst is selected because of its effect on the nitrogen content in the diamond synthesized with Fe or Ni based catalyst, and the elimination method of microcrystalline graphite precipitation is presented by analyzing its mechanism. Fourthly, the boron elements exist in IIb-type diamond and have influence on the growth characteristics of synthetic diamond. Fifthly, introduced is the research status of diamond synthesized with B, N, S, P doping elements, in which its individual substance or their compound is used as a doping source or boron and other elements with small radius are used as co-doping agent. Then S or P with B co-doping is more conducive to the improvement of the performance of n-type diamond large single crystal semiconductor. Therefore, it is proposed that the large diamond single crystal need strengthening in mass production of IIa-type large diamond single crystal, superconducting characteristics of IIb-type large diamond single crystal, and doping of n-type semiconductors.