Cosmological topological defects are predicted in a large class of particle physics models and they provide unique access to physics at the highest energy scales and the earliest moments of the universe. Fortunately, topological defects such as cosmic strings lead to an array of observational signatures that are within the scope of different observational efforts, including the detection of gravitational waves, the cosmic microwave background, gamma rays bursts, cosmic rays, fast radio bursts and potentially the cosmological 21 cm background. Crucially, the search for these signatures is motivated and enabled by predictions that arise from modelling of the topological defects and their dynamics. The focus of the workshop is to establish and clarify the dynamics of cosmic strings, about which there has been some disagreement, and to predict more robust observational signatures especially relevant to LIGO and the Pulsar Timing Array. The workshop will also be relevant in other systems where defect dynamics is important, such as neutron stars and QCD axions.