  The past 5 years have dramatically changed our view of the disks of gas and
dust around young stars. Observations with the Atacama Large
Millimeter/submillimeter Array (ALMA) and extreme adaptive optics systems have
revealed that disks are dynamical systems. Most disks contain resolved
structures, both in gas and dust, including rings, gaps, spirals, azimuthal
dust concentrations, shadows cast by misaligned inner disks, as well as
deviations from Keplerian rotation. The origin of these structures and how they
relate to the planet formation process remain poorly understood. Spatially
resolved kinematic studies offer a new and necessary window to understand and
quantify the physical processes (turbulence, winds, radial and meridional
flows, stellar multiplicity, instabilities) at play during planet formation and
disk evolution. Recent progress, driven mainly by resolved ALMA observations,
includes the detection and mass determination of embedded planets, the mapping
of the gas flow around the accreting planets, the confirmation of tidal
interactions and warped disk geometries, and stringent limits on the turbulent
velocities. In this chapter, we will review our current understanding of these
dynamical processes and highlight how kinematic mapping provides new ways to
observe planet formation in action.
