The KymoKnot software package and webserver identifies and locates physical knots or proper knots in a series of polymer conformations. It mainly intended as analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally-invasive chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The webserver offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .