Moiré materials are a class of highly tunable, strongly correlated two-dimensional (2D) materials formed by the rotational or lattice misalignment of atomically thin crystals. These materials host flat electronic bands that significantly enhance Coulomb interactions, leading to exotic electronic phases with robust topological properties. Local spectroscopic, thermodynamic, and electromagnetic probes have been crucial in identifying mechanisms behind these phases, including correlated insulators, unconventional superconductors, moiré ferroelectrics, and topological orbital ferromagnets. Recent local probe techniques, such as local charge sensing and quantum interference probes, have uncovered new physical observables in moiré materials. Moiré materials exhibit rich, tunable phase diagrams, with examples including magic-angle twisted bilayer graphene (MATBG), twisted bilayer MoTe₂, and aligned WSe₂/WS₂. These materials display a variety of correlated insulating phases, such as Mott insulators and generalized Wigner crystals (GWCs), as well as unconventional superconducting phases and topological insulators. The flat electronic bands in moiré materials enable strong electronic correlations, leading to phenomena like orbital ferromagnetism and quantum anomalous Hall effects. Local probe techniques, such as scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and microwave impedance microscopy (MIM), have provided detailed insights into the electronic structure and phase transitions in moiré materials. These techniques allow for the visualization of complex quantum phases, including charge-ordered states and topological insulators, and have revealed the importance of symmetry-breaking in these systems. The combination of these techniques has enabled the identification of correlated insulators, such as those in MATBG and MATTG, and has provided a deeper understanding of the electronic mechanisms underlying these materials. The study of moiré materials has revealed the importance of flat electronic bands in enabling strong electronic correlations and topological properties. These materials offer a unique platform for exploring strongly interacting quantum systems and have the potential to lead to new technological applications. The use of local probe techniques has been instrumental in uncovering the complex electronic phases and mechanisms in moiré materials, providing a foundation for further research and development in this field.Moiré materials are a class of highly tunable, strongly correlated two-dimensional (2D) materials formed by the rotational or lattice misalignment of atomically thin crystals. These materials host flat electronic bands that significantly enhance Coulomb interactions, leading to exotic electronic phases with robust topological properties. Local spectroscopic, thermodynamic, and electromagnetic probes have been crucial in identifying mechanisms behind these phases, including correlated insulators, unconventional superconductors, moiré ferroelectrics, and topological orbital ferromagnets. Recent local probe techniques, such as local charge sensing and quantum interference probes, have uncovered new physical observables in moiré materials. Moiré materials exhibit rich, tunable phase diagrams, with examples including magic-angle twisted bilayer graphene (MATBG), twisted bilayer MoTe₂, and aligned WSe₂/WS₂. These materials display a variety of correlated insulating phases, such as Mott insulators and generalized Wigner crystals (GWCs), as well as unconventional superconducting phases and topological insulators. The flat electronic bands in moiré materials enable strong electronic correlations, leading to phenomena like orbital ferromagnetism and quantum anomalous Hall effects. Local probe techniques, such as scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and microwave impedance microscopy (MIM), have provided detailed insights into the electronic structure and phase transitions in moiré materials. These techniques allow for the visualization of complex quantum phases, including charge-ordered states and topological insulators, and have revealed the importance of symmetry-breaking in these systems. The combination of these techniques has enabled the identification of correlated insulators, such as those in MATBG and MATTG, and has provided a deeper understanding of the electronic mechanisms underlying these materials. The study of moiré materials has revealed the importance of flat electronic bands in enabling strong electronic correlations and topological properties. These materials offer a unique platform for exploring strongly interacting quantum systems and have the potential to lead to new technological applications. The use of local probe techniques has been instrumental in uncovering the complex electronic phases and mechanisms in moiré materials, providing a foundation for further research and development in this field.