To understand how the smallest known particles in our universe form structures, scientists need to use sophisticated mathematical models and techniques. These help scientists to estimate the energies of these particles, to work out how they combine and interact. In a recent paper, Dr Eef Van Beveren from the Centre for Physics of the University of Coimbra and Dr George Rupp from the Centre of Physics and Engineering of Advanced Materials of the University of Lisbon review the techniques that have led to scientific discoveries about mesons – subatomic particles that exist for tiny fractions of a second. They also discuss how such techniques may evolve into the future.