A stunning range of substructures in the dust of protoplanetary disks is routinely observed across a range of wavelengths. These gaps, rings and spirals are highly indicative of a population of unseen planets, hinting at the possibility of current observational facilities being able to capture planet-formation in action. Over the last decade, our understanding of the influence of a young planet on the dynamical structure of its parental disk has progressed significantly, revealing a host of potentially observable features which would betray the presence of a deeply embedded planet. In concert, recent observations have shown that subtle perturbations in the kinematic structure of protoplanetary disks are found in multiple sources, potentially the characteristic disturbances associated with embedded planets. In this work, we review the theoretical background of planet-disk interactions, focusing on the kinematical features, and the current methodologies used to observe these interactions in spatially and spectrally resolved observations. We discuss the potential pit falls of such kinematical detections of planets, providing best-practices for imaging and analysing interferometric data, along with a set of criteria to use as a benchmark for any claimed detection of embedded planets. We finish with a discussion on the current state of simulations in regard to planet-disk interactions, highlighting areas of particular interest and future directions which will provide the most significant impact in our search for embedded planets. This work is the culmination of the 'Visualizing the Kinematics of Planet Formation' workshop, held in October 2019 at the Center for Computational Astrophysics at the Flatiron Institute in New York City.