Trapped wave phenomena are challenging to analyse and predict, as they usually require the study of partial differential equations with one or more complications from complex boundaries, variable co-efficients or non-linearity. The workshop brought together researchers whose expertise spans geophysical flows, surface water waves, complex dynamics and experiments, and the underpinning theory of waves in fluids. These specialists came from different fields: pure and applied mathematics, atmospheric and ocean scientists, experimentalists and industry representatives. This workshop was a perfect environment for them to exchange ideas, borrow approaches and start interdisciplinary collaborations. Additionally, it identified and outlined outstanding mathematical problems underpinning wave trapping and wave radiation.