Understanding strongly correlated topological quantum phases has been a longstanding challenge. Moiré materials present a unique opportunity as they allow us to engineer flat topological bands and vary the carrier density throughout entire bands in situ using electrostatic gates. I will open the talk by presenting nanoscale images of equilibrium currents in quantum Hall edge states in monolayer graphene​1​ and magic-angle twisted bilayer graphene (MATBG)​2​, a strongly correlated moiré system, acquired using a scanning superconducting quantum interference device on a tip. Surprisingly, we found that edge states in MATBG appear in the bulk rather than along the edges. This unique behavior is due to disorder in the twist-angle that we map accurately, highlighting the significance of a local band structure. In the second part of my talk, I will show experiments that extend the moiré paradigm to multi-moiré systems. By twisting trilayer graphene with two alternating but unequal twist angles, we engineered a moiré quasicrystal formed by two incommensurate moiré patterns​3​. By gating, we tuned in and out of a quasiperiodic regime, where we observed isospin symmetry breaking and superconductivity. In contrast, in trilayer graphene twisted sequentially in the same direction by the same angle, we found anomalous Hall effect at odd integers and fractional filling factors, with no signatures of superconductivity​4​. There, lattice relaxation forms large supermoiré periodic regions that spontaneously break ?2?�2 symmetry, giving rise to local Chern bands. I will discuss the implications of our findings and future directions.