Electrons in many solid materials, despite of their Coulomb interactions, can be qualitatively treated as non-interacting quasiparticles, a concept central to Fermi-liquid theory, established by Lev Landau in the 1950s. However, an increasing number of novel quantum phenomena, especially those related to unconventional superconductivity, fractional quantum Hall effects, charge density wave, and Luttinger liquid physics, cannot be captured in this Fermi-liquid framework because of the strong electron correlations. Albeit with research over decades, our understanding of non-Fermi liquid physics in quantum materials remains far from complete. In this talk, I will introduce and discuss fascinating new opportunities allowed by two-dimensional (2D) materials and moiré systems for investigating non-Fermi liquid behaviors in strongly correlated electronic systems. I will talk about our recent observation of moiré Luttinger liquids in small-angle twisted tungsten ditelluride (WTe2). The result demonstrates that the Luttinger liquid physics, often expected for interacting one-dimensional systems, can also survive in an anisotropic 2D system. It encourages the search for novel fractionalized quasiparticles, such as spinons and holons, in the 2D WTe2 system. The talk will also cover innovative approaches in material and device design, measurement techniques, and applying extreme conditions to further our understanding of strongly correlated quantum phenomena in 2D materials.