Thanks to advances in in situ measurement techniques for electrical transport in ultra-high vacuum together with emergent materials such as Rashba-type surfaces, topological insulators, atomic-layer superconductors, and 2D materials like graphene, surface states and edge states on crystals provide intriguing topics, e.g. dissipation-less currents, spin-polarized electric current, and pure spin current. This is due to broken symmetry and strong spin–orbit and electron–phonon interactions. Here we review some examples of experimental techniques of multi-probe methods at macroscopic and microscopic scales, followed by transport phenomena revealed by them. These are opening a field in condensed matter physics driven by symmetry breaking at surfaces and atomic layers.