Baryons are considered in the Nonrelativistic Quark Model (NQM) to be bound states of three valence quarks. Each quark has two possible spin eigenstates in the restframe of the baryon whose spin is fully carried by quarks. The baryon wavefunctions are connected through SU(6) symmetry rotations. For a long time, the measured magnetic moments of the baryons appeared to be in agreement with the NQM predictions. However, recent experiments which are examining the spin structure of the baryons show the failure of several NQM predictions. The so-called 'spin crisis' arose from the interpretation of the EMC deep inelastic scattering measurement of ∫ g^p₁ that the quark spins in the proton appeared to sum up to (almost) zero. In this thesis it will be demonstrated that the spin problem is not a phenomenon restricted to quasi-massless current quarks in the high energy limit. Symmetry arguments are used to examine the baryon magnetic moments and reveal that we can observe massive but pointhke constituent quarks, with a characteristic mass ratio m_u = m_d ≃ ²andfrasl;₃m_s. Surprisingly they do not contribute much to the baryon spin either. This analysis is free of the ambiguity arising from the UA(1} gluon anomaly which makes it impossible to calculate precisely the spin sum of the current quarks. One important finding in our analysis is the observation that the effects of SU(6) breaking hyperfine spin-spin interactions (which cause well-known splittings in the baryon masses) can be seen in the environment dependence of the constituent quark masses. The effective mass of a quark cannot be independent of its surrounding energy since the mass of the baryon is distributed amongst its constituents. Consistent with the hypothesis that different quark masses do not impose SU(3) breaking on the baryon wavefunctions is the observation of induced 'second class' form factors. The way in which SU(3) breaking alters the ^g_Aandfrasl;_{g_V} ratios in semileptonic hyperon decays will be discussed and strong evidence for a new value of F/D is given, which is close to its SU(6) value. This value is derived independently from the baryon β-decays <strong>and</strong> from their magnetic moments. Dynamical models are discussed which might explain the observed polarised strangeness 'inside' the proton, and the almost vanishing quark spin sum.