  Quasi-low-dimensional (quasi-low-D) inorganic materials are not only ideally
suited for angle resolved photoemission spectroscopy (ARPES) but also they
offer a rich ground for studying key concepts for the emerging paradigm of
non-Fermi liquid (non-FL) physics. In this article, we discuss the ARPES
technique applied to three quasi-low-D inorganic metals: a paradigm Fermi
liquid (FL) material TiTe$_{2}$, a well-known quasi-1D charge density wave
(CDW) material K$_{0.3}$MoO$_{3}$ and a quasi-1D non-CDW material
Li$_{0.9}$Mo$_{6}$O$_{17}$. With TiTe$_2$, we establish that a many body
theoretical interpretation of the ARPES line shape is possible. We also address
the fundamental question of how to accurately determine the {\bf k}$_F$ value
from ARPES. Both K$_{0.3}$MoO$_{3}$ and Li$_{0.9}$Mo$_{6}$O$_{17}$ show
quasi-1D electronic structures with non-FL line shapes. A CDW gap opening is
observed for K$_{0.3}$MoO$_{3}$, whereas no gap is observed for
Li$_{0.9}$Mo$_{6}$O$_{17}$. We show, however, that the standard CDW theory,
even with strong fluctuations, is not sufficient to describe the non-FL line
shapes of K$_{0.3}$MoO$_{3}$. We argue that a Luttinger liquid (LL) model is
relevant for both bronzes, but also point out difficulties encountered in
comparing data with theory. We interpret this situation to mean that a more
complete and realistic theory is necessary to understand these data.
