The renormalization group was originally introduced as a multiscale approach to quantum field theory and the theory of critical phenomena, explaining in particular the universality observed e.g. in critical exponents. Since then it has become a hugely important tool in statistical mechanics, condensed matter and high energy physics. More recently, renormalization has also played a decisive role in mathematics as a method of proof, applicable in quantum field theory, differential equations, probability, and other fields. The workshop has focused on new developments along the lines of these two traditions. Besides discussing methodical progress and current applications, we have explored new challenges and problems that may in the future be tackled with the help of the renormalization group.