I will talk about both numerical simulations and observations of protoplanetary disks. I will start with numerical simulations of disk-planet interactions in protoplanetary disks. Particularly, I will discuss the damping of the density waves excited by planets due to the nonlinearity in their propagation, which can result in gap opening in a low viscosity disk by low mass planets. Then I will move on to observations of transitional disks, which are protoplanetary disks with central depleted regions (cavities). Several ideas on the formation of transitional disks have been proposed, including gaps opened by planet(s). Recently, Subaru directly imaged a number of such disks at near infrared (NIR) wavelengths (the SEEDS project) with high spatial resolution and small inner working angles. Using radiative transfer simulations, we study the structure of transitional disks by modeling the NIR images, the SED, and the sub-mm observations from literature (whenever available ) simultaneously. We obtain physical disk+cavity structures, and constrain the spatial distribution of the dust grains, particularly inside the cavity and at the cavity edge. Interestingly, we find that in some cases cavities are not present in the scattered light. In such cases we present a new transitional disk model to simultaneously account for all observations. Decoupling between the sub-um-sized and mm-sized grains inside the cavity is required, which may necessitate the dust filtration mechanism. For another group of transitional disks in which Subaru does reveal the cavities at NIR, we focus on whether grains at different sizes have the same spatial distribution or not. We use our modeling results to constrain transitional disk formation theories, particularly to comment on their possible planets origin.