A group is called polycyclic if it has a subnormal series with cyclic factors. This characterisation can be used to design effective and practical algorithms for polycyclic groups. For finite polycyclic groups such methods have been developed over the last 30 years and they are used successfully in computations with finite polycyclic groups. The infinite case is much less investigated and it is the aim of this talk to report on some recent developments in the design of practical algorithms for (possibly infinite) polycyclic groups.