Through this review we can follow the various phases that have led to the discovery of the new allotrope form of silicon: silicene. This is a one-atom thick silicon sheet arranged in a honeycomb lattice, similar to graphene. For silicon, which usually is sp3 hybridized, it represents an unusual and rare structure. First, silicene was theoretically hypothesized and subsequently its structure calculated as a possible candidate for nano-ribbons of Si grown on the anisotropic Ag(110) surface. It was only later, when the physical and chemical properties of this peculiar form of silicon, demonstrating the presence of π and π* bands giving the so-called Dirac cones at the K corners of the Brillouin zone, the sp2-like nature of the valence orbitals of the Si-Si bonds and its strong resistance towards oxygen were reported, that the real existence of silicene became recognized in the scientific community. This review is essentially focused on the experimental work performed on 1D isolated silicene nano-ribbons and their 1D dense array grown on Ag(110) surfaces.