Abstarct: Due to the importance of analytical solution in various constituent quark models and also due to the importance of relativistic effects of quarks dynamics in investigation of the internal structure of baryons, our efforts has been dedicated, to a better and more precise modeling of quarks dynamics in baryons, in first step, and to insert the relativistic effects, in next step. So, after a detailed review of the hypercentral constituent quark model, we presented some improved nonrelativistic and semi-relativistic three-quark models for investigating the internal structure of the light and strange baryons. baxsed on hypercentral approach, we considered the baryons as a three-body bound system without spin and isospin degrees of freedom and solved the relevant three-body Schrödinger and Klein-Gordon equations analytically. Thoroughly, we obtain the dominant SU(6)-invariant spectrum which accounts for the average multiplet energies. Then we treated the spin- and isospin (flavour)-dependent interactions perturbatively. Due to the fact that there is not exact analytical solution of Schrödinger (and Klein-Gordon) equation for the well-known “linear-plus-Coulombic” potential, we developed a suitable approximation for the problematic linear confining term so that the modified potential is suitable for analytical purposes. In semi-relativistic case, we considered equal (different) scalar and vector potentials, and solved the three-body Klein-Gordon equation approximately (exactly). In both nonrelativistic and semi-relativistic cases, the analytically obtained energy eigenvalues and eigenfunctions of the three-body problem have been used in the calculations of the mass spectrum of baryons and electromagnetic elastic form factors of nucleon. The magnetic moments and charge radii of nucleon have also been calculated. We have compared the evaluated observables with experimental data and it has been shown that the presented models provide a good descxription of the observed resonances.