In van der Waals heterostructures composed of two rotated graphene sheets, a moiré superlattice results in the emergence of flat electronic bands over a small range of twist angles. A variety of highly tunable correlated and topological states have recently been identified in these platforms owing to the quenched kinetic energy of charge carriers and the intrinsic Berry curvature of the flat bands. I will discuss our recent work investigating these states in three different twisted graphene platforms. In twisted bilayer graphene – two rotated monolayer graphene sheets – we observe correlated insulating states and superconductivity for twist angles very near 1.1°. These states are exquisitely sensitive to the twist angle, and can be further tuned dynamically within a single device by electrostatic doping or with hydrostatic pressure. In twisted double bilayer graphene – two rotated sheets of Bernal-stacked bilayer graphene – correlated states can be additionally controlled by an external electric field, and consequentially manifest over a wider range of twist angles. Finally, in twisted monolayer-bilayer graphene, we observe a novel form of ferromagnetism driven primarily by the formation of spontaneous orbital currents rather than the long-range ordering of electron spins. Owing to the non-trivial topology of the bands, the orbital ferromagnetism is additionally accompanied by signatures of an incipient quantum anomalous Hall state. Overall, our results demonstrate the extraordinary tunability of correlated and topological states in twisted graphene heterostructures.