The suction between soil particles is the basis and core problem in the study of unsaturated soil. However, is the suction between soil particles just the matrix suction (which has been widely used since the discipline of unsaturated soil mechanics was established). In fact, the concept of matrix suction is from soil science and reflects the water-absorbing capacity of the soil. Matrix suction characterizes the interaction between soil particles and pore water rather than the interactions between soil particles, which were not in conformity with the principle of effective stress of soils. The suction of unsaturated soil, in essence, is the intergranular suction composed of absorbed suction and structural suction. In this paper, first, the basic concepts of absorbed suction and structural suction were briefly introduced. Then, with soil mechanics, powder science, crystal chemistry, granular material mechanics and other related disciplines of knowledge for reference, the quantitative calculation formulas were theoretically deduced for the absorbed suction for equal-sized and unequal-sized unsaturated soil particles with arbitrary packing and the variable structural suction for equal-sized unsaturated soil particles with arbitrary packing and unequal-sized unsaturated soil particles with close tetrahedral packing. The factors that influence these equations were discussed. Then, the shear strength theory of unsaturated soil was established based on the theory of intergranular suction through the analysis of the effective stress principle of unsaturated soil. This study demonstrates that the shear strength of unsaturated soil consists of three parts: The effective cohesive force, the additional strength caused by external loads and the strength caused by intergranular suction. The contribution of the three parts to the shear strength of unsaturated soil depends on the following influence factors: Soil type, confining pressure, water content and density. Therefore, these factors must be comprehensively considered when determining the strength of an unsaturated soil.