This dissertation explores the rich interplay of strong correlation and topological physics in transition metal dichalcogenide (TMD) moiré superlattices. Moiré superlattices, formed by stacking two slightly misaligned layers of TMDs, emerge as a versatile simulation platform for condensed matter physics. The moiré periodic potential significantly modifies the electronic band structure, leading to flat bands and consequently strong electron correlation effects. Moreover, by judicious choice of stacking configurations to allow for the intertwining of two moiré bands, non-trivial topological states can be realized. We exploit these unique features to experimentally study a variety of correlated and topological phenomena.The thesis is structured around two TMD moiré systems. We begin with the AA-stacked WSe2/WS2 moiré superlattice, one of the first TMD moiré systems that demonstrates a strong correlation effect. We unravel the electronic stripe phases, a direct consequence of the competition interactions, and examine the influence of strong correlation on exciton behavior, leading to unusual electron-exciton interactions. From Chapter 4 onwards, we shift our attention to the AB-stacked MoTe2/WSe2 moiré structure. This system maps to a single-band extended Hubbard model at low electric fields and features a rich phase diagram with non-trivial topology at high electric fields. We study kinetics magnetism and the emergence of spin polaron in the moiré Hubbard system in Chapter 4. Further, a comprehensive phase diagram is presented in Chapter 5, followed by an in-depth examination of the quantum anomalous Hall state in Chapters 6 and 7.