Electronic structure methods based on density-functional theory, pseudopotentials, and local-orbital basis sets offer a hierarchy of techniques for modeling complex condensed-matter systems with a wide range of precisions and computational speeds. We analyze the relationships between the algorithms for atomic forces in this hierarchy of techniques, going from empirical tight-binding through ab initio tight-binding to full ab initio. The analysis gives a unified overview of the force algorithms as applied within techniques based either on diagonalization or on linear-scaling approaches. The use of these force algorithms is illustrated by practical calculations with the CONQUEST code, in which different techniques in the hierarchy are applied in a concerted manner. (C) 2004 American Institute of Physics.