Plant-macrofossil analysis is being increasingly used in Quaternary science, particularly palaeoecology and vegetation history. Although the techniques of macrofossil analysis are well-tried and relatively simple, the resulting data consisting of qualitative binary presences and absences, ordinal classes, and quantitative counts are not simple from the viewpoint of numerical data-analysis. This essay reviews the nature of macrofossil data and discusses the problem of zero and non-zero values. Problems in the presentation of macrofossil data are outlined and possible solutions are discussed. The handling of such data is discussed in terms of data summarisation, data analysis, and data interpretation. Newly developed numerical methods that take account of the mixed nature and the stratigraphical ordering of macrofossil data are outlined, such as (distance-based) multivariate regression trees, canonical analysis of principal coordinates, principal curves, cascade multivariate regression trees, and RLQ analysis. These and other techniques outlined have the potential to help exploit the full potential of macrofossil stratigraphical data in Quaternary palaeoecology.