Recent discoveries on Mott insulating and unconventional superconducting states in twisted bilayer graphene with moiré superlattices have not only reshaped the landscape of "twistronics", but also sparked the rapidly growing fields of moiré photonic and phononic structures. These innovative moiré structures have revealed new routes of exploration for classical wave physics leading to intriguing phenomena and robust control of electromagnetic and mechanical waves.

Drawing inspiration from the success of twisted bilayer graphene, this perspective casts an overarching framework of the emerging moiré photonic and phononic structures that promise novel classical-wave devices. We begin with the fundamentals of moiré superlattices, before highlighting recent works that exploit twist angle and interlayer coupling as new ingredients to engineer and tailor the band structures and effective material properties of photonic and phononic structures. We finally discuss future directions and promises of this emerging area in materials science and wave physics.