Many of the mountain valleys in the Alps have glaciers at their heads. When Swiss geologist Louis Agassiz examined the valleys around his home, he noticed that the debris near the glacier, clearly put there by the ice, resembled the debris further down the valley. In other words, the glacier had been further down the valley in the past. The only mechanism he could imagine was that it had been colder at some time in the past.

As he expanded his examination, he found similar debris all over Europe. He concluded that ice must have covered most of the continent at some time in the past.

Agassiz published his findings in his 1840 work Étude sur les glaciers, and in the 1847 work Système glaciare. In 1846, Agassiz moved to the United States and started looking for evidence of glaciation in North America. And he found his evidence, lying all over.

Evidence for ice ages occurs throughout the geological record. A massive ice sheet covered large parts of the Gondwana continent through much of the Paleozoic Era, and a controversial (but plausible) "Snowball Earth" theory suggests that the Earth was completely covered by ice several times during the Precambrian.

Historically, four main ice ages were thought to have occured during the last 4.5 million years or so, the Pleistocene epoch. As has been reported elsewhere, it is now known that continental ice sheets have advanced and retreated many more than 4 times during the Pleistocene. Depending upon how big your requirement for an "ice age" is, there have been as many as 45 of them. But these four episodes represent the largest glacial maxima that have left traces on the Earth, and are thus of the most interest to people studying the Earth's surface. Various names have been given these episodes, where they have affected different regions of the Earth:

Alps      | Europe      | North America | China  
Gunz      | Menapian    | Nebraskan     | Po-Yang
Mindel    | Elsterian   | Kansan        | Ta-Gu
Riss      | Saalian     | Illinoian     | Lu-Shan
Würm      | Weichselian | Wisconsin     | Ta-Li

To climatologists, it's all part of a continuous fluctuation of Earth's climate, and we happen to be in a relatively warm period at the moment. Relative to the recent past. Other periods of geological history were much warmer than now, and it's reasonable to assume there will be warmer periods in the future. Only human conceit has caused us to separate the last 10,000 years into its own epoch, the Holocene. When asked "when will the next Ice Age come?", it's perfectly reasonable to answer "We're in an Ice Age right now".