Two-dimensional (2D) materials, such as graphene, are atomically thin crystals exfoliated from layered materials. Recent developments have enabled scientists to isolate 2D materials with various electronic properties and assemble them into van der Waals heterostructures with elaborate stacking and precise crystalline alignments. This ability to construct materials layer-by-layer has allowed engineering of the band structure and interactions of electrons to cultivate novel quantum states of matter. A plethora of emergent quantum phases have been discovered in various 2D platforms, spanning correlated electron states, unconventional superconductivity and topological states of matter. Despite intensive studies they have attracted, many important questions remain. Scanning tunneling microscopes, with the energy and spatial resolution, can shed light on these questions. In this talk, I will demonstrate scanning tunneling microscopy and spectroscopy as powerful tools to probe emergent electron orders in 2D systems, focusing on moire flat band systems and the graphene quantum Hall system.