More than 17 years have passed since the invention of the scanning tunneling microscopy, and the development of scanning probe microscopies is now so rapid and remarkable. Moreover the impact has been so great to activate the novel researches in the fields of surface science and nano-structure science. In this article we briefly review present status of the theoretical bases of SPM and future problems. In particular we focus on the theory of quantum transport of atom/molecular bridges and the basic mechanism of the noncontact atomic force microscopy.