This thesis presents the results of a concerted effort to understand the complex array of physical properties exhibited by the BaVS3 family of materials. As a 3d1 system, BaVS3 displays a unique collection of correlation-driven phenomena, including a metal-insulator transition driven by spin-density waves and or charge-density waves as well as a pressure-dependent crossover between the non-Fermi-liquid and Fermi-liquid behaviors. In an attempt to better understand these and many other properties, we have undertaken a systematic experimental study of BaVS3 and related compounds. The primary measurements carried out were those of the transport properties, resistivity and thermoelectric power (TEP). Through the construction of specialized measuring apparatuses, we were able to measure simultaneously these transport properties under conditions of variable temperature (from 2 to 600 K), pressure (up to 3 GPa) and magnetic field (up to 12 T). At ambient pressure and in the range of 250 to 600K, BaVS3 shows nearly isotropic but poor metallic behavior with linear temperature dependences of resistivity and TEP and a Curie-like magnetic susceptibility. The nearly isotropic conductivity contrasts with the 1D 2kF fluctuations observed by lowering the temperature below 250 K (at which the first Jahn-Teller structural phase transition occurs) deep in the metallic phase. The fluctuations reveal the 1D aspects of the electronic character, originating from the chain like structure of the material. The salient feature of BaVS3 at ambient pressure is the second order metal-to-insulator (MI) transition at TMI = 69 K, accompanied by the tetramerization (doubling of the 2V unit cell in the chain direction). In addition to the transport measurements, the strong changes in the electrical and magnetic properties of the system around TMI were followed by magnetic susceptibility, angle-resolved photoelectron spectroscopy and frequency-dependent conductivity. By increasing the pressure, the three-dimensionality of BaVS3 is enhanced and the MI phase transition is suppressed to lower temperatures. TEP and magneto TEP measurements in this pressure range revealed the existence of polarons and of spin fluctuations in the metallic phase. The latter can be identified as precursors to the MI transition. Around 1.8 GPa, where TMI ~15 K, the system enters a strongly fluctuating regime, highly sensitive to the magnetic field, the amplitude and the frequency of the measuring current and to a further increase of the pressure. Closely related to these features, the phase boundary collapses and a hysteretic behavior appears in the transport properties and their magnetic-field-dependent counterparts. At a critical pressure of ~2 GPa, a non-Fermi liquid (NFL) state arises (with n~1.5 in the Tn resistivity law between 1 and 15 K) in relation to the proximate Quantum Critical Point. The p-H-T phase diagram of BaVS3 in this region has been explored in some detail with particular emphasis placed upon the relevance of the spin degrees of freedom (on the insulator side) and the role of quantum fluctuations above the critical pressure. Finally, as the pressure is increased further, the conventional Fermi-liquid exponent of n = 2 is obtained. In order to delve further into the subtleties of the MI transition and the NFL behavior, a comparative study was carried out on the sister compounds Bax-1SrxVS3 and BaVS3 and on sulfur-deficient BaVS3. From this study it became apparent that the imposed chemical substitution manifests itself as an additional effective pressure. The inherent disorder of these samples was observed to affect the NFL behavior by reducing the exponent n towards a value of 1, while the apparent ferromagnetic order below 15 K was seemingly independent of pressure. All the observed features are consistent with a relatively simple two-band tight-binding, vanadium-based, model consisting of a wide quasi one-dimensional band hybridized with a rather isotropic narrow band. Within this context, it is concluded that the MI transition is controlled by the Coulomb-interacting electrons of the wide quasi one-dimensional band. Based on this model a new description of the NFL regime has been proposed.