Abstract: A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact. Granular materials are omnipresent in nature, industrial practice and daily life, with size spanning from 1 $\muup$m to a few meters. The mechanical properties have long been studied. In recent two decades, many laboratory scale tests have been conducted and novel phenomena were observed. Both theoretical studies, such as granular matter statistical mechanics, granular solid hydrodynamics, and measurement techniques, such as X-ray CT, photoelastics, have witnessed great breakthrough. The revealed physical mechanism prompt ones to examine the assumptions, concepts, models and theories that previously proposed and being used. In this review paper, major fundamental problems are presented introduced and discussed, including the characteristics of microscale structure, procedure of micro-macro study with Rowe stress dilatancy relation as an example, derivation of stress and strain from microscale structure, the relation of macroscale strength with particle friction, size effect and similarity. In addition, granular soil as a typical granular material, its new developments are summarized. The frequently used techniques are introduced as well. Finally, we present a few aspects in which research should be reinforced, such as examining the assumptions in the discrete element method and checking the computing details, conducting the ideal physical and numerical experiments; by lying on the fast development of high performance computing, carrying on high scientific confidence degree large scale computation of granular materials with high scientific confidence degree; with the help of fast development of high performence computers. The mechanics of granular materials is still at its infancy stage, and there is a long way to directly solve the engineering problems. Essential development of related engineering technologies depends certainly on progress or break-through in the of fundamental studies of granular material mechanics.