Electrons in many solid-state materials, despite of their Coulomb interactions, can be qualitatively treated as non-interacting quasiparticles. This is in particular the Fermi-liquid theory, which was introduced by Lev Landau in the 1950s and has been the foundation of quantum condensed matter physics. However, an increasing number of novel quantum phenomena, especially those related to unconventional superconductivity, fractional quantum Hall effects 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. As a highlighted example, 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. Finally, I will also discuss the need of new methods for discovering and investigating strongly correlated quantum phenomena based on 2D materials, including aspects of new material and device designs, new measurement techniques, and the application of extreme conditions.