Topological materials present opportunities for understanding new fundamental physics and achieving novel devices which may be facilitated through the realization of exotic states such as Majorana fermions and magnetic monopoles. When the electrons in topological materials are confined to atomically thin dimensions, quantum size effects can alter greatly their properties. Here, we discuss two experimental realizations of topological thin films, Sb and Bi2Te3, and demonstrate explicitly the topological order by angle-resolved photoemission spectroscopy (ARPES). The quantum tunneling effect in films opens a thickness-dependent energy gap at the Dirac point of the topological surface bands. Our ARPES measurement and first-principles calculation show that the tunneling energy gap and topological surface band dispersion can be controlled through surface engineering. In addition, we probe the electronic chirality and Berry's phase in graphene and the spin-texture in Bi/Ag surface alloy by the method of circular photoemission. These results are of fundamental interest for understanding unique electronic and spin properties of topological thin films, and further provide a promising basis for thin-film device applications.