Abstract During times of continental glaciation (e.g. Pennsylvanian-Early Permian, Miocene-Pleistocene), parasequences on carbonate platforms appear to be dominated by 400, 100 and possibly 40 ka Milankovitch climatic and eustatic changes with 50–100 m shifts in sea level. Carbonate cycles have conspicuous regional disconformities and associated aeolianites, lack tidal-flat facies except near the continental shoreline, commonly have deeper-water facies sandwiched between shallow-water deposits, and there is much unfilled accommodation. The large changes in sea level in ice-house times causes ramps to have significant gradients, thus on high-energy ramps, there can be widespread grainstone sheets. Platform tops have much depositional relief (pinnacle reefs and mounds) and erosional topography. Cycles may be highly shingled and show major lateral shifts on the ramp from cycle to cycle. During times with moderate continental ice sheets (e.g. late Mid- to Late Ordovician, Early Carboniferous), ramp cycles lack deeper-water facies, rarely have regional tidal flats but instead show widespread disconformities updip and some aeolianites. The only tidal-flat facies are developed within third-order highstand systems tracts (perhaps reflecting decreased amplitude, higher-frequency eustasy) or in downdip positions during fourth-order lowstands. Margins show moderate shingling. Grainy reservoir facies are regionally extensive, as a result of moderately large shifts of grainstone belts. Grainy facies in downslope build-ups are compartmentalized by muddy incipient drowning facies. Storm beds on the deep ramp are arranged in upward-coarsening units because of high-frequency eustasy. During global greenhouse times and little global ice (e.g. Late Cambrian-Early Ordovician, Devonian, Triassic, Cretaceous), parasequences updip on aggraded ramps are dominated by roughly 20 ka precessional cycles that formed under small (possibly <10 m or so) sea-level fluctuations, possibly coupled with an autocyclic component. The cycles typically consist of very shallow-water facies, with regional tidal flat caps and minor disconformities; cycles form layer-cake successions on the shallow ramp, and may be bundled into 100 and 400 ka sets, although ‘missing beats’ on the platform commonly obscure simple ratios typical of Milankovitch forcing. The ramps commonly have very low gradients and platforms tend to be aggraded with little topography, unless sedimentation rates are low, which results in poorly cyclic, subtidal skeletal facies over much of the ramp. Any compartmentalization of downslope subtidal build-ups is due to long-term incipient drowning events.