More and more underground coal and metal mines have been developed intoa deep level. Withincrease of mining depth, a series of engineering catastrophes such as rockburst, coal and gas burst,collapse of roof strata and water burst from floor strata are gettingmore serious and more frequent. In addition,supporting and retaining theory of tunnel and stope in the depths aredifferent from the ones at a shallow levels.Such a difference is caused by the difference of geological environmentsbetween deep and shallow levels.The most distinguished differences between deep and shallow levels arethe  so-called three ``highs'', i.e., highcrustal  stress, high earth temperature and high pore pressure. Underhigh crustal stress, rocks showsome special mechanical behaviors. In this paper, the current state ofunderground mining in the depths,technical difficulties of deep mining and geological environment of highcrustal stress of rocks in the depths areintroduced. Moreover, the developments in researches on mechanicalbehaviors of rocks in the  depths arereviewed, including brittle-ductile transition, time-dependent behavior, strength features and failurebehaviors especially rockburst  under the condition of high crustal stress. At the end of the paper, itis pointed out that the thermal-mechanical-hydrological coupling model under the conditions of deepmining is an attractive topic.