Besides the mere tracking of individual particles through an accelerator lattice, it is often helpful to study the corresponding phase‐space map relating initial and final coordinates. Recent years have seen an advance in the ability to compute high‐order maps for rather complex systems including accelerator lattices. Besides providing insight, the maps allow treatment of the lattice without approximations, allowing thick elements, fringe‐field effects and even radiation, which is often prohibitive in the case of pure tracking. At the core of the computation of maps for realistic systems are the differential algebraic (DA) techniques.Besides the computation of maps, the DA methods have recently proven useful for the computation of many properties of the maps in a rather direct way. In particular, these properties include parameter tune shifts, amplitude tune shifts, and pseudo invariants. The methods presented here do not rely on Lie algebraic methods and are noticeably more direct and in many cases more efficient. Not relying on canonical techniques, they are also applicable to non‐symplectic systems and allow a study of damping phenomena in repetitive systems.