Electronic properties of low-dimensional systems — and particularly quasi-one-dimensional systems — together with related correlated electron phenomena have for quite some time been at the very frontier of condensed matter physics. The interest ranges from purely fundamental reasons, since the reduced dimension offers a unique possibility of direct calculation of many-body problems, to nowadays very intense interest in functional nano-systems. Angle-resolved photoemission spectroscopy (ARPES) is arguably the most direct probe of the physical properties of solids, which arise from low-energy electronic excitations. With the present state-of-the-art high energy/angle resolution detectors, it allows a direct insight into the most subtle effects of electron correlations. All the results presented in this Thesis are the first ARPES measurements on several inorganic chain-like materials that are, or are related to Peierls conductors. These quasi-one-dimensional correlated materials typically exhibit non-Fermi liquid like properties that are at the same time incompatible with any of the existing singular Fermi liquid scenarios (such as Luttinger liquid). In that respect the aim is twofold: to reveal the new physics arising from direct electronic structure measurements, and secondly, to compare the emerging models for the spectroscopic features with the new findings. More specifically, the Thesis focuses on the influence of the electron-phonon coupling on the observed excitations. A quasi-one-dimensional insulating compound K0.33MoO3, known as molybdenum red bronze, is closely related to the blue bronze K0.3MoO3, a 1D Peierls conductor. We disclose the details of the electron structure and reveal the important role of defect induced states. The small mobile polaron scenario describes well the blue bronze, and this picture is further strengthened, as we discuss here, by the spectroscopic similarities with the red bronze. Then we present measurements on two transition metal trichalcogenides: ZrTe3 and TaSe3. The first is a Peierls compound whose peculiar Fermi surface hides its low-dimensional character. The latter, strikingly, even though it does not exhibit any instability, shows spectroscopic similarities with the Peierls conductors, thereby demonstrating the importance of electron-phonon interactions in this material, as well as the general importance of the particularities of the Fermi surface in setting the conditions for an electronic instability. Finally, we report the results on one of the most intriguing materials in the field — BaVS3. This correlated electron system demonstrates a wealth of complex, poorly understood phases. Extensive experimental findings cannot easily be put together into a coherent picture. Our direct electronic structure measurements suggest that the puzzling electronic properties are due to the interplay of the 1D states and a narrow localized band. We find supporting evidence for a one-dimensional instability driving the metal-insulator transition at 69 K and propose its realization through a mechanism of interband nesting. We conclude that there is a direct link between the observed non-Fermi liquid features and the intrinsic characteristics of 1D Peierls conductors and/or one-dimensionality in general. The influence of electron-phonon coupling in conjunction with the reduced dimensionality leads to spectroscopic features that hide the realizations of the singular behavior. However, a detailed modeling of the new data presented here is necessary to place them in the framework of the emerging theories.