In this paper we discuss the state of the art of describing the structure and dynamics of crystal surfaces at the atomic level. Depending on the type of processes that one wants to describe, different approaches are to be chosen. We focus on equilibrium surface structures at the scale of typical growth units during growth or melting. For atomic crystals these length scales are Angstroms, for nano-crystals and organic molecules, nanometres, for colloids and proteins up to 10-100nm. The challenge is to find a reliable description of a growth unit and its environment that is computationally cheap, informative and involves as little neighbouring growth units as possible. We explain how the environment of a growth unit can be defined, how we found optimal local order parameters, and we discuss some published and some new results. Our discussion is based on molecular simulation, mostly of Lennard-Jones crystals. (c) 2004 Elsevier B.V. All rights reserved.