In 1895, G.K. Gilbert suggested that rhythmical repetition of patterns in the sequences of strata correspond to orbital variations and could provide a chronology for Earth history. This suggestion remained a heuristic hypothesis in need of testing; in this, the Mediterranean region latterly played a crucial role. Its extended sequences of pelagic and lacustrine–paludal strata provide long time series of hierarchical rhythmic variations tied directly to biostratigraphy and to magnetic reversals. The latter provide historical control and links to astronomically calculated curves that have been extended progressively into the past. These comparisons verify the orbital origins of the major sedimentary rhythms and are serving to reduce the age uncertainties of the significant time stratigraphic levels (biostratigraphic and magnetostratigraphic zones) from an order of ca 500 kyr toward the precessional (20 kyr) level. This refinement has essentially been reached for the last 14 Myr of Earth history in the Mediterranean, and beyond in the Pacific Ocean. The cyclic structure of shallow-water platform carbonates is also hierarchical but here the identification with specific orbital cycles has been equivocal and complicated by conflicts with radiometric data. In the gap-riddled shallow-water successions showing hierarchical ‘sequences’, the identification of some third-order, fourth-order and fifth-order ‘sequences’ or ‘parasequences’ with orbital forcing is being explored but remains inferential. Beyond chronology, the orbital variations constitute an endless series of experiments: similar variations in insolation, which resulted in sedimentary patterns formed by a chain of responses extending through atmospheric and hydrospheric dynamics to geological processes and the dynamics of the biotic systems. The emerging patterns offer glimpses into the past, to reveal previously unexpected phenomena such as systematic oscillations in deep-water aeration and unexpected oscillations in composition of upper-water plankton: patterns that pose new challenges to the understanding of Earth history.