1 Baryons and the three-body problem
 1.1 Who is afraid of the three-body problem ?
 1.2 Old, present, and future baryon spectroscopy
 1.3 Outline of the review
 1.4 A guide to related references
2 The two-body problem
 2.1 Basic equations
 2.2 Properties of the wave functions
 2.3 Scaling laws
 2.4 Numerical solutions
 2.5 Semi-classical approximation
 2.6 Level order
 2.7 Mass dependence of the binding energy
3 The harmonic-oscillator model
 3.1 The linear oscillator
 3.2 The spatial oscillator
 3.3 Three-body oscillator with equal masses
 3.4 Permutation of three quarks
 3.5 Colour, spin, and isospin wave functions
 3.6 Spatial wave functions of given permutation symmetry
 3.7 Harmonic oscillator with unequal masses
4 Variational methods
 4.1 Introduction
 4.2 General properties of variational solutions
 4.3 Harmonic-oscillator expansion (equal masses)
 4.4 Harmonic oscillator expansion (unequal masses)
 4.5 Empirical variational methods
 4.6 Short-range correlations
 4.7 Improved variational methods
5 The hyperspherical formalism
 5.1 Basic formalism
 5.2 The hyperspherical harmonics
 5.3 The radial potentials
 5.4 The coupled equations
 5.5 Results
 5.6 Extension to unequal masses
6 Faddeev equations
 6.1 Basic equations
 6.2 Solving the Faddeev equation
 6.3 Numerical solution of the Faddeev equations
 6.4 Results
7 Quark–diquark and Born–Oppenheimer approxiamtions
 7.1 The diquark–quark approximation
 7.2 The Born–Oppenheimer approximation
8 Level order
 8.1 Nearly harmonic potentials
 8.2 Nearly hyperscalar potentials
 8.3 Lowest excitation
9 Mass inequalities
 9.1 Mass dependence of the three-body binding energy
 9.2 Relation between the quark–antiquark and the quark–quark potentials
 9.3 Simple lower bound on baryon energies
 9.4 Improved lower bounds
 9.5 Comparison of the wave functions
 9.6 Connection to physical mesons
 9.7 The case of unequal constituent masses
 9.8 Generalization to excited states
10 Bounds on short-range correlations
 10.1 Generalized Schwinger rule
 10.2 The case of linear confinement
 10.3 Correlations for more general potentials
11 Some applications to baryon spectroscopy
 11.1 Ground-state baryons with central potentials
 11.2 Systematics of hyperfine splittings
 11.3 Hyperfine splitting of heavy baryons
 11.4 Electromagnetic mass differences
 11.5 The charge radius of the neutron
 11.6 The quadrupole moment of the Omega
 11.7 Outlook