In spite of the fact that thermal conductivity is a key factor in basin modelling, knowledge regarding the thermal conductivity of sedimentary rocks is scarce. In particular, hardly any information exists about claystones and mudstones which can make up 70-80% of a sedimentary basin. For the Upper Jurassic sediments of a section across the northern North Sea, basin modelling programs, using the geometric mean model, gave a deviation of 50~ for the present-day temperature, simply because the matrix conductivity was estimated by two different models. These uncertainties in the determination of thermal conductivities are partly due to problems in measuring, and partly to difficulties in modelling the thermal conductivity. Future work should concentrate on comparative studies and tests on all types of sedimentary rocks, directed towards improved measurement methods. This is of particular importance for clays, mudstones and shales, as measurements on these are associated with the greatest uncertainties. Standardized procedures that include detailed descriptions of sampling, sample preparation and measurement techniques are important to ensure that the thermal conductivity measured is unaffected by factors related to the measurement method. In thermal conductivity modelling it is our experience that the influence of sediment texture is underestimated by most models currently applied. Estimates based on the geometric mean model seem to be most reliable when the determination of matrix conductivity is restricted to the sediment type, mineralogy and texture of the sediments.