Although the aim of this review is to discuss elaborate methods for solving the three-body problem, the very simple harmonic-oscillator model deserves some presentation. First, it has played an essential role in the development of the quark model, with, in particular, the pioneering works of Dalitz [34] and Greenberg [4] and the very complete and convincing studies of the baryon spectrum by Dalitz and Horgan [35], Isgur and Karl [36], Gromes et al.[37], Cutkosky and Hendrick [38], Hey et al.[6] and many others [39]. The harmonic-oscillator model may also serve as a basis or a starting point for accurate variational methods. Its understanding is anyhow necessary for getting some insight into the three-body problem and, in particular, into the difficulties associated with the symmetrization of the wave functions.