Dust and gas in protoplanetary disks are the building blocks of planets. In this thesis, we study the dynamics of the gas and dust, which are crucial for the planet formation theory, using observational and numerical approaches. The observational part contains the case study of a rare circumtriple disk around the GW Ori hierarchical triple system. We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of 1.3 mm dust continuum and 12CO J = 2-1 molecular gas emission of the disk. For the first time, we identify three dust rings in the GW Ori disk at ~46, 188, and 338 au, with the outermost ring being the largest dust ring ever found in protoplanetary disks. We use visibility modeling of the dust continuum and kinematics modeling of CO lines to show that the disk has misaligned parts, and the innermost dust ring is eccentric. We interpret these substructures as evidence of ongoing dynamical interactions between the triple stars and the circumtriple disk. In the numerical part, we study whether or not dust around gas gaps opened by planets can remain settled by performing three-dimensional, dust-plus-gas simulations of protoplanetary disks with an embedded planet. We find planets that open gas gaps 'puff up' small, sub-mm-sized grains at the gap edges, where the dust scale-height can reach 80% of the gas scale-height. We attribute this dust 'puff-up' to the planet-induced meridional gas flows previously identified by Fung and Chiang. We thus emphasize the importance of explicit 3D simulations to obtain the vertical distribution of sub-mm-sized grains around planet gaps. We caution that the gas-gap-opening planet interpretation of well-defined dust rings is only self-consistent with large grains exceeding mm in size. / Graduate