  The discoveries of numerous exciting phenomena in twisted bilayer graphene
(TBG) are stimulating significant investigations on moir\'e structures that
possess a tunable moir\'e potential. Optical response can provide insights into
the electronic structures and transport phenomena of non-twisted and twisted
moir\'e structures. In this article, we review both experimental and
theoretical studies of optical properties such as optical conductivity,
dielectric function, non-linear optical response, and plasmons in moir\'e
structures composed of graphene, hexagonal boron nitride (hBN), and/or
transition metal dichalcogenides (TMDCs). Firstly, a comprehensive introduction
to the widely employed methodology on optical properties is presented. After,
moir\'e potential induced optical conductivity and plasmons in non-twisted
structures are reviewed, such as single layer graphene-hBN, bilayer
graphene-hBN and graphene-metal moir\'e heterostructures. Next, recent
investigations of twist-angle dependent optical response and plasmons are
addressed in twisted moir\'e structures. Additionally, we discuss how optical
properties and plasmons could contribute to the understanding of the many-body
effects and superconductivity observed in moir\'e structures.
