My interest in least-cost path (LCP) calculations developed when adjusting an algorithm for density clustering. The aim was to identify central places and to allocate all other sites to these central places, based on the assumption that the central places are areas of high interaction (Herzog 2009a; 2013c). In general, the estimation of the interaction between two sites depends on the distance between the two locations considered (Rodrigue *et al*. 2009, 216–18). Axel Posluschny provided test data consisting of the Hallstatt and Urnfield Culture sites in the Main triangle, Germany, for the density clustering algorithm. The initial algorithm was based on straight-line distances, and it was felt that the cost distances are more appropriate in this terrain. So in a second step an adjustment was planned to include the cost distances into the calculation. As the cost-distance based density clustering was to be carried out by one computer program, the GIS software available could not be used. After a glimpse at the GIS reference book for archaeologists by Conolly and Lake (2006), a first LCP component was programmed – which created strange results. So it became necessary to collect and study the relevant references in more detail, and the present article is one of the outcomes of those endeavours.

Section 2 below will outline different applications of spatial analysis in archaeology that either use cost distances or could be extended to take path costs into account. LCP algorithms are discussed in Section 3. These algorithms rely heavily on the cost distance calculations, therefore Section 4 deals with properties of least-cost distances. Several components like slope, water travel or vegetation cover can be combined to calculate cost distances (Section 5). Nearly all archaeological LCP studies apply one of a set of different slope-based cost functions, with or without taking the direction of movement into account. A large subsection of this article discusses the different issues and approaches to slope-dependent cost modelling. Subsequent subsections cover other possible cost components, such as vegetation cover or travelling and transport on water that are applied less frequently in archaeological cost calculations. A section on combining cost components is followed by the conclusions.