We give a pedagogical overview of exciting quantum phenomena that are unique to two-dimensional electron solids. The uniqueness arises from the role of the quantum phase that influences various remarkable attributes such as the relativistic Rashba interaction, the Berry curvature, quantum Hall effect, magnetic oscillation, etc., which are intimately connected to Landau diamagnetism and the concomitant Aharonov–Bohm phase. These attributes are characteristics of two-dimensional quantum solids such as graphene, interfaces of oxides and some topological insulators. Because these material properties hinge on the interplay of the intrinsic spin of the electron with its motion, the resultant field is known as Spintronics.