Atomic gases can be cooled down to extremely low temperatures (a few nano-Kelvin above absolute zero) when they start behaving as quantum fluids. The physics of these systems has advanced considerably over the past decade because experiments can trap such ultracold gases in versatile geometries, their interactions can be tuned, and they can be kept isolated from the environment for sufficiently long times to preserve their quantum nature. These advances have opened the possibility to experimentally realize one-dimensional atomic gases so that they behave as quantum abacus beads. Such peculiar quantum systems of many particles can in some cases be theoretically understood exactly, which is not the case for most quantum systems. This gives an unprecedented opportunity to investigate strongly correlated states of matter, in and out of equilibrium, both theoretically and experimentally. We will present a general introduction of these systems and our selected results based on exact solutions in these systems. Finally, it will be shown that besides probing low dimensional quantum gases, these systems hold the potential to realize models in more than three dimensions.