Mechanism theory, synthesis and control of robots, rigid body dynamics, geometrically exact formulations of the kinematics of continua, structure preserving numerical integration methods, and in part geometric mechanics - they all have a common denominator, namely the theory of screws, for which Lie group theory forms the mathematical foundation. This paper is an attempt to provide a short survey identifying several scientific areas where screw theory is already (sometimes implicitly) used and such where its systematic application could lead to new formulations and computational algorithms. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim).