Abstract: Recently commissioned telescopes and instruments (e.g., Subaru, GPI, VLA, ALMA, EVLA) are now finally able to resolve the protoplanetary disk down to the AU scale, and a rich variety of disk features have been revealed: gaps, large scale disk asymmetry, and spiral arms. To confront these observations, theoretical models need to be developed so that we can use observations to constrain the physics of disk structure and planet formation. In the talk, I will summarize our recent progress on planet-disk interaction study, focusing on explaining the observed spirals and how a single planet can lead to multiple gaps. To directly find young planets, I will argue that disks around these forming planets, so-called circumplanetary disks, could be the key and we may have already found some circumplanetary disk candidates. Finally, I will present our latest global 3-D MHD simulations of accretion disks to study disk accretion and disk winds. Such simulations reveal surprising accretion and outflow patterns which may have important theoretical and observational implications.