Graphene moiré structures provide a paradigm system to study correlated physics and superconductivity in the 2D limit. A simple twist between graphene layers gives rise to a unique energy band structure, where strong Coulomb correlation unlocks a rich landscape of quantum ground states such as correlation-driven insulators, superconductivity, and ferromagnetism. Here I will show results from recent experiments which are designed to directly study the role of Coulomb correlation and extract thermodynamic properties of the moiré flatband. I will discuss the implications of these findings on our understandings of graphene moiré systems.