Vortices in superconducting tunnel junctions are magnetic flux quanta which propagate with relativistic velocities and have characteristic properties of solitons. The book is starting from a very basic introduction into both physics of superconductors and modeling of solitons and moving on to a more advanced review of the state-of-the-art of the field in the final chapters. It will be of interest both to people who are new to studies of vortex dynamics in Josephson junctions and to those who are already familiar with this fascinating area of research. This field puts together solid state physics, electromagnetism and nonlinear dynamics of waves. The author, who is himself an experimentalist, concentrates on experimental and physical aspects rather than on mathematical theory of solitons. While the introduction focuses on the Josephson effect along with the modeling of solitons in Josephson systems, the main part of the book deals with topics such as the observation methods for Josephson solitons, different regimes of vortex motion, various geometries of junctions and arrays of them. Most recent and advanced topics as quantum dynamics of Josephson vortices, stacks, and applications of solitons oscillators are discussed at the final part of the book.