One-dimensional (1D) forms of conduction channels in nanometer scale is an essential ingredient of nano and molecular electronics. Based on, particularly, silicon substrates, we have investigated the growth and physical properties of self-organized metallic atomic chains or nanowires. In fundamental points of view, some of these atomic chains (nanowires) on silicon surfaces have been found to have very interesting electronic properties based on their 1D metallic band structures, namely the Peierls instability of metallic phases. The notable recent examples are 4x1-In on Si(111) [1-4], 1x2-Au on Si(5 5 7) [5], Si(5 5 12) [6] and Si(5 5 3) [7, 8], and GdSix on Si(001) [9]. In the present talk, I will discuss (i) the 1D or quasi-1D band structures of these systems, (ii) the generic instability of their metallic phases, (iii) the intrinsic fluctuations on the 1D metallic systems, and (iv) the local and global effects of defects. The experimental works are based on high-resolution angle-resolved photoemission and variable-temperature scanning tunneling microscopy/spectroscopy. These studies unveil the atomic-scale details of the physics of 1D or quasi-1D metals through its metal-insulator phase transitions, which may guide the future application of the nano-/atomic-wires.