Surface states that are inherent in surface superstructures, provide unique platforms for studying low-dimensional electron systems, exhibiting some aspects of many-body effects, in phase transitions, for example. Electronic transport is a key for such physics, too. First, I present direct detections of electrical transport through the surface-state bands on silicon, by in-situ measurements in UHV with macroscopic four-point probes,@footnote 1@ microscopic ones,@footnote 2,3@ and four-tip STM.@footnote 4@ The influences of atomic steps and domain boundaries on the conductivity were directly measured. Next, I present characteristic changes in surface conductivity at a surface phase transition.@footnote 5@ A Si(111)-8x2-In surface at 100K is believed to be a charge-density-wave (CDW) phase.@footnote 6@ By adding small amounts of impurity atoms on it, the CDW phase was destroyed, accompanied with steep increases in conductivity. This means that the metalicity of the surface is recovered by this change; the impurity atoms act as electronic disturbers. @FootnoteText@ @footnote 1@ S. Hasegawa, et al., Prog. Surf. Scie. 60 (1999) 89. @footnote 2@ I. Shiraki, et al., Surf. Rev. Lett. 7 (2000) 533. @footnote 3@ C. L. Petersen, et al., Appl. Phys. Lett. 77 (2000) 3782. @footnote 4@ I. Shiraki, et al., Surf. Scie. (2001) in press. @footnote 5@ S. V. Ryjkov, et al., Surf. Scie (2001) in press. @footnote 6@ H.-W. Yeom, et al., Phys. Rev. Lett. 82 (1999) 4898.