The Earth's climate switches between "hothouse Earth", where ice is nearly absent worldwide, and "icehouse Earth" where the Earth intermittently has ice that stretches far from the poles. Periods when the Earth is in the icehouse Earth phase are called ice ages. The most recent ice age began about 2.6 million years ago and has not yet ended. We are still in an ice age, as evidenced by the fact that Antarctica and Greenland are still covered by ice. Ice ages last many tens to a few hundred of millions of years.
Ice ages are characterized by glacial periods where ice reaches far from the poles separated by interglacial periods where the climate is a bit more moderate. The glacial and interglacial periods within an ice age last tens to hundreds of thousands of years. The current interglacial period began about 12,000 years ago. It's the Milankovitch cycles that are responsible for the short duration glacial and interglacial periods within an ice age.
These cycles are still present when the Earth is in a hothouse Earth phase. The Earth was in the hothouse phase for about 250-260 million years before the current ice age. That's 2000 or so multiples of the very longest Milankovitch cycle. The Milankovitch cycles are not responsible for the hothouse Earth / icehouse Earth phases. It's plate tectonics that dictates whether Earth is in a hothouse Earth or icehouse Earth phase.
So what aspects of plate tectonics govern whether the Earth is in a hothouse phase or icehouse phase? Below are a series of images depicting how the Earth looked over recent times.
35 million years ago, hardly any ice anywhere.
20 million years ago, just a tiny bit of ice in the very far north and very far south.
Current ice age, (~2.6 million years ago to present), with ice sometimes reaching as far as 45° latitude.
Source: Ron Blakey, via wikimedia.org. (Blakey's maps are 1200x600, which is a bit wide. I used the 640x320 previews at wikimedia.org.)
There are two key differences at the boundaries of the Pacific Ocean between the pre-ice age Earth and our current ice age Earth. One is the Indonesian seaway. That closed up 3 to 4 million years ago thanks to New Guinea, Indonesia, and the Malay Peninsula. The other is the Panama seaway. That closed up about 3 million years ago thanks to the formation of the Isthmus of Panama. The closing off of the Pacific near the equator drastically changed the global ocean conveyor belt, which in turn drastically changed the climate of the Earth.
So which of these two seaway closures, if any, is the cause of the most recent switch from hothouse Earth to icehouse Earth? A number of researchers put the blame on the formation of the Isthmus of Panama (Bartoli 2005, Nie 2014). Others claim the closure of the Indonesian seaway was responsible (Cane and Molner 2001, Molner 2008). Yet others say "none of the above" (Lunt 2008). The jury is still out, but note that Smith and Pickering 2003 claim that plate tectonics are responsible for each of the four major icehouses in the last 620 million years.
Bartoli, G., et al. (2005). "Final closure of Panama and the onset of northern hemisphere glaciation." Earth and Planetary Science Letters, 237.1: 33-44.
Blakey, Ron. cpgeosystems.com/paleomaps.html (website)
Cane, Mark A., and Peter Molnar (2001). "Closing of the Indonesian seaway as a precursor to east African aridification around 3–4 million years ago." Nature 411.6834: 157-162.
Lunt, Daniel J., et al. (2008). "Late Pliocene Greenland glaciation controlled by a decline in atmospheric CO2 levels." Nature 454.7208: 1102-1105.
Molnar, Peter (2008). "Closing of the Central American Seaway and the Ice Age: A critical review." Paleoceanography 23.2.
Nie, Junsheng, et al. (2014). "Pacific freshening drives Pliocene cooling and Asian monsoon intensification." Scientific Reports 4.
Smith, Alan G., and Kevin T. Pickering (2003). "Oceanic gateways as a critical factor to initiate icehouse Earth." Journal of the Geological Society 160.3: 337-340.