The Milankovitch theory of climate change is widely accepted, but the registration of the climate changes in the stratigraphic record and their use in building high-resolution astronomically tuned timescales has been disputed due to the complex and fragmentary nature of the stratigraphic record. However, results of time series analysis and consistency with independent magnetobiostratigraphic and/or radio-isotopic age models show that Milankovitch cycles are recorded not only in deep marine and lacustrine successions, but also in ice cores and speleothems, and in eolian and fluvial successions. Integrated stratigraphic studies further provide evidence for continuous sedimentation at Milankovitch time scales (104 years up to 106 years). This combined approach also shows that strict application of statistical confidence limits in spectral analysis to verify astronomical forcing in climate proxy records is not fully justified and may lead to false negatives. This is in contrast to recent claims that failure to apply strict statistical standards can lead to false positives in the search for periodic signals. Finally, and contrary to the argument that changes in insolation are too small to effect significant climate change, seasonal insolation variations resulting from orbital extremes can be significant (20% and more) and, as shown by climate modelling, generate large climate changes that can be expected to leave a marked imprint in the stratigraphic record. The tuning of long and continuous cyclic successions now underlies the standard geological time scale for much of the Cenozoic and also for extended intervals of the Mesozoic. Such successions have to be taken into account to fully comprehend the (cyclic) nature of the stratigraphic record.