Growing amount of molecular biological data combined with current advances in modeling of complex systems provide unprecedented opportunities to understand biological evolution in a quantitative way. A quantitative description of an evolving system is the first step towards prediction and control, and it opens new exciting directions for highly interdisciplinary research. The central questions are: (i) to what degree we can predict the outcome of biological evolution, (ii) what features of the system are predictable and (iii) which features confer predictive value for a quantitative description of the system. This program brings together theoretical and experimental physicists, experimental biologists with an interest in quantitative modelling and mathematicians with interest in biological systems. We aim to create a dialog between researchers of different fields and to inspire future collaborations. In addition, further developments in this field would have significant translational impacts, e.g., by optimizing vaccines against evolving viruses, designing strategies for personalized cancer therapy and by providing insights to the problem of antibiotic resistance.