Moiré materials have emerged as a platform for exploring the physics of strong electronic correlations and non-trivial band topology. Here we review the recent progress in semiconductor moiré materials, with a particular focus on transition metal dichalcogenides. Following a brief overview of the general features in this class of materials, we discuss recent theoretical and experimental studies on Hubbard physics, Kane-Mele-Hubbard physics and equilibrium moiré excitons. We also comment on the future opportunities and challenges in the studies of transition metal dichalcogenide and other semiconductor moiré materials.