Free boundary problems are today considered as one of the most important directions in the mainstream of the analysis of partial differential equations (PDEs), with an abundance of applications in various sciences and real world problems. In the last two decades, various new ideas, techniques, and methods have been developed, and new important, challenging problems in physics, engineering, industry, finance, biology, and other areas have arisen. The topics of this programme are at the forefront of current exciting developments. We realise that there have been few activities on free boundary problems in recent decades in the UK. We strongly believe that a thematic programme at the Newton Institute will have a huge impact on the development of FBPs from all points of view. The programme is directed towards theory, numerics and applications. It will further enhance the interaction between UK mathematicians and top international researchers in this field and strengthen the UK expertise in FBPs. Read more at www.newton.ac.uk/programmes/FRB/