The elementary properties of one-dimensional (1D) excitons in GaAs quantum wires (QWRs) in the strong-confinement regime have been reviewed in order to investigate the novel physics inherent to 1D systems. We first overview the energy levels realized in various QWRs such as T-shaped, V-groove, vicinal-substrate, and post-growth-etching QWRs. Then we study lateral confinement energy, exciton binding energy, the Bloch part and the envelope part of the wave functions, oscillator strength, lifetime, laser action, and other properties such as many-body effects and relaxation processes. A set of experimental data are given as examples, mostly taken from the recent work on T-shaped QWRs by the author and co-workers, and there is some discussion of these data.