  The hypercentral Constituent Quark Model (hCQM) for the baryon structure is
reviewed and its applications are systematically discussed. The model is based
on a simple form of the quark potential, which contains a Coulomb-like
interaction and a confinement, both expressed in terms of a collective space
coordinate, the hyperradius. The model has only three free parameters,
determined in order to describe the baryon spectrum. Once the parameters have
been fixed, the model, in its non relativistic version, is used to predict
various quantities of physical interest, namely the elastic nucleon form
factors, the photocouplings and the helicity amplitudes for the electromagnetic
excitation of the baryon resonances. In particular, the $Q^2$ dependence of the
helicity amplitude is quite well reproduced, thanks to the Coulomb-like
interaction. The model is reformulated in a relativistic version by means of
the Point Form hamilton dynamics. While the inclusion of relativity does not
alter the results for the helicity amplitudes, a good description of the
nucleon elastic form factors is obtained.
