Much of our understanding of Earth's past climate states comes from the measurement of oxygen and carbon isotope variations in deep-sea benthic foraminifera. Yet, major intervals in those records that lack the temporal resolution and/or age control required to identify climate forcing and feedback mechanisms. Here we document 66 million years of global climate by a new high-fidelity Cenozoic global reference benthic carbon and oxygen isotope dataset (CENOGRID). Using recurrence analysis, we find that on timescales of millions of years Earth's climate can be grouped into Hothouse, Warmhouse, Coolhouse and Icehouse states separated by transitions related to changing greenhouse gas levels and the growth of polar ice sheets. Each Cenozoic climate state is paced by orbital cycles, but the response to radiative forcing is state dependent.