The application of numerical techniques within palaeoentomology has been sporadic and of a largely simplistic nature. In particular, the assessment of faunal similarity has relied mainly upon subjective value judgements; similarly, the reconstruction of past climates using fossil Coleoptera has been undertaken with only a limited application of numerical methods. This thesis presents a computational approach to these problems. Although the intrinsic properties of palaeoentomological sample units impose limitations on the validity of a statistical analysis of faunal similarity, the use of such techniques is fully justifiable. Several methods have been tested with a wide range of data, using intuitive interpretations as reference standards. Binary data, in conjunction with a limited combination of clustering techniques and resemblance coefficients, produce results which compare favourably with the traditional assessments; numeric data and Principal Components Analysis are useful in difficult analytical situations and / or when particularly complex questions are being asked. To enable palaeoclimatic reconstructions to be produced quickly and accurately a computer package of Fortran programs has been written and implemented. By representing the geographical range of a beetle on climatic axes it is possible to derive estimates of the past thermal climate from an assemblage of fossil beetles. Using the Mutual Climatic Range Reconstruction Package the thermal climate of Britain during the Late Quaternary has been examined in detail. The pattern correlates with that derived from ocean care data, being characterised by abrupt changes between contrasting climatic states. The climatic reconstruction methodology has been inverted to provide a means whereby potential coleopteran faunas can be derived for particular thermal climates. In the context of the origin of the invertebrate faunas of the N. Atlantic Islands, the results of the Pest program provide support for a glacial tabula rasa followed by immigration via ice rafting at c. 10,000 B. P., as opposed to the alternative hypothesis of glacial survival in refugia.