Two-dimensional (2D) material research is rapidly evolving to broaden the spectrum of emergent 2D systems. Here, we review recent advances in the theory, synthesis, characterization, device, and quantum physics of 2D materials and their heterostructures. First, we shed insight into modeling of defects and intercalants, focusing on their formation pathways and strategic functionalities. We also review machine learning for synthesis and sensing applications of 2D materials. In addition, we highlight important development in the synthesis, processing, and characterization of various 2D materials (e.g., MXnenes, magnetic compounds, epitaxial layers, low-symmetry crystals, etc.) and discuss oxidation and strain gradient engineering in 2D materials. Next, we discuss the optical and phonon properties of 2D materials controlled by material inhomogeneity and give examples of multidimensional imaging and biosensing equipped with machine learning analysis based on 2D platforms. We then provide updates on mix-dimensional heterostructures using 2D building blocks for next-generation logic/memory devices and the quantum anomalous Hall devices of high-quality magnetic topological insulators, followed by advances in small twist-angle homojunctions and their exciting quantum transport. Finally, we provide the perspectives and future work on several topics mentioned in this review.
Keywords: 2D Materials; Biosensing; Doping; Epitaxial Growth; Machine Learning; Magnetic and Topological Properties; Moiré Engineering; Multidimensional Heterostructures; Strain Engineering; Theory.