Over the last three decades a large number of experimental studies on several quasi onedimensional (1D) metals and quasi 1D Mott-Hubbard insulators have produced evidence for distinct spectral features identified with charge-only and spin-only fractionalized particles. They can be also observed in ultra-cold atomic 1D optical lattices and quantum wires. 1D exactly solvable models provide nontrivial tests of the approaches for these systems relying on field theories. Different schemes such as the pseudofermion dynamical theory (PDT) and the mobile quantum impurity model (MQIM) have revealed that the 1D correlated models high-energy physics is qualitatively different from that of a lowenergy Tomonaga-Luttinger liquid (TLL). This includes the momentum dependence of the exponents that control the one-and two-particle dynamical correlation functions near their spectra edges and in the vicinity of one-particle singular spectral features.On the one hand, the low-energy charge-only and spin-only fractionalized particles are usually identified with holons and spinons, respectively. On the other hand, ''particlelike'' representations in terms of pseudoparticles, related PDT pseudofermions, and MQIM particles are suitable for the description of both the low-energy TLL physics and highenergy spectral and dynamical properties of 1D correlated systems.The main goal of this review is to revisit the usefulness of pseudoparticle and PDT pseudofermion representations for the study of both static and high-energy spectral and dynamical properties of the 1D Lieb-Liniger Bose gas, spin-1/2 isotropic Heisenberg chain, and 1D Hubbard model. Moreover, the relation between the PDT and the MQIM is clarified. The fractionalized particles and related composite pseudoparticles/pseudofermions emerging within such non-perturbative 1D correlated systems are qualitatively different from the Fermi-liquid quasiparticles. In contrast to the holons and spinons, the relation to the electron creation and annihilation operators of the operators associated with the 1D Hubbard model three fractionalized particles is uniquely defined. The occupancy configurations of such fractionalized particles generate all energy and momentum eigenstates of that model. Both the static and dynamical properties of the three models under review are shown to be controlled at all energy scales by pseudofermion phase shifts associated with only zero-momentum forward scattering. The corresponding microscopic processes are much simpler than those of the underlying particles non-perturbative interactions.